Congratulations on your kaba gaida! Before I attempt to answer your questions let me say this: The gaida returns what you put into it. It requires regular playing and maintenance and is not an easy instrument to learn. However, if you stick with it the reward is well worth it.
I am assuming you are from the west (somewhere in the Americas) judging by the time of your post (Bulgaria would be sleeping). If so, hopefully I can help you with your questions and lessons learned from my experience.
The gaida should be stored in a plastic bag like a 13 gallon trash bag. You can store the gaida in a leather pouch. However, plastic really is better, and it should be stored in a plastic bag inside the leather pouch. Humidity and temperature directly affect the gaida as its an ancient instrument made of wood and leather. In Bulgaria, its recommended to store the gaida wrapped in plastic in the механа "mehana" or basement. The basements there stay around 60 degrees F and provide a good environment for the instrument. I live in Texas, and we don't have basements. So I store my gaida in a plastic bag and put it in a cabinet. Out of sunlight and out of direct flow of A/C or heaters in the house. You can store your instrument in a case or chest, but I strongly recommend putting it in a plastic bag first. It is very important that your reeds and pipes do not dry out. They have natural oils, and oils/fats that you must add, to keep them functioning (I will address this later).
To put your gaida up, you leave the chanter in the horn and the first segment of the drone attached to the bag. This way the reeds (inside these two pipes) are still inside the bag. Next, deconstruct the other two pieces of the drone (the second and third segments). Flatten the bag by pushing air out of it. Place the now detached segments of the drone and lay them in the center of the deflated bag. Next take the chanter and the first segment of the drone (both still attached to the bag) and fold them in with the other two segments. Now all 4 segments (2 attached, and 2 detached) are all lined up in a small bundle in the middle of the flattened bag. Fold/Roll the bag around the pipes like a burrito. In the end you should have the pipes in the middle, and the bag around them.
When you play, never take the chanter (gaidunitza) out and play it like a whistle/flute. Its very very bad to get saliva directly on the reed as you would with a clarinet or other woodwind instruments - the gaida reed is not the same. Getting saliva on the reed will make it too damp and will eventually dry it out like chapped lips. Always blow up the bag (even to practice) and play with the chanter in the bag. If you play the gaidunitza directly you will ruin the reed. I did this to my first reed - trust me - bad idea.
Don't worry too much about condensed water in the bag. Traditional gaidas are made from goat skin and are salt cured. If you have a tradition bag (it will have a thick skin) the bag will naturally absorb your warm breath and any condensed water. This keeps the bag loose. I was fortunate enough to take a few lessons from Petar Yanev over the summer. He plays up to 8 hours a day and goes through bags every few months. However he assured me not to worry about natural water or sweat on/in the bag. Some gaidars take a shot of rakia (brandi), you could use vodka, and poor a shot into the bag after they played for hours. The alcohol evaporates quickly and it will kill microorganisms in the bag. This really isn't necessary for people that aren't playing hours and hours on end, and you don't need to do it.
Do not remove the reeds from the chanter or drone to dry them out. Keep them in the pipes and keep the pipes in the bag - only play that way. For practice you should not be using the drone. Take a cork from a wine bottle, cut it to fit, and plug up the drone. This way air only flows out of the chanter. You can see Cvetelin playing this way in his training videos on youtube. I know its tempting to plug the drone in and play. Don't do it. You must first learn to balance your breaths and play steady with just the chanter as he is showing. If you play with the drone as a beginner it will stunt your learning curve.
There really is no better substitute to tallow or suet. I was instructed to use suet, which is beef kidney fat. Its hard at room temperature but will become malleable in your hands. Suet/Tallow is what the master gaidars use. You can get suet at butcher shops, apparently its not an uncommon ingredient in American chilli. Store the suet in the refrigerator in a plastic bag. To lube the reeds, take a small piece in your fingers - about the size of a grain of rice. Let the suet warm up on your fingers and then rub the threaded section of the reed. The threads will absorb the fat and the reed will absorb it from the threads. Do not apply the suet directly to the reed. You can wipe off your fingers, when there is no more visible fat left on them, onto the reed. Your fingers will be sticky. If you apply the fat as a chunk directly to the reed it can cause the reed to stick to itself and affect the playability. Its really best to just apply the fat to the threads and as your last wipe - so to speak - apply it to the reed itself.
You can lubricate the reed before every time you play. The threads should always be sticky. That helps the reed seal itself in the pipe and keep the reed hydrated as it will draw out any fat it needs. You can apply quite a bit of fat to the threads as long as there aren't visible chunks left and you work the fat in. Petar Yanev did not recommend using beeswax unless its a last resort. Ive used it and it doesn't work nearly as well. Its hard and not very malleable. I did end up using Burt's Bees all natural chapstick (made from beeswax) before I met him. Its better than straight beeswax for hydration. But I strongly *strongly* recommend you use fat (tallow/suet).
You will also need to lubricate your pipes. If you live in a dry climate, lubricate them more often. I posted on here about what the best oil is to use for the pipes. Check out that conversation for more detail. Almond and olive oil are good oils to use. Almond oil has a higher flash point and lasts longer. Its more expensive but worth it. Heat the oil up and poor it on the pipes. Work it in with a cloth and let them sit/drip for 15 minutes.
Tuning the gaida can be a real challenge and could take alot of typing to explain. First, before you start messing with the reeds make sure that the top part of the reed (the flap) is facing 90 degrees to the left of the front holes. If you insert the reed with the flap facing the front holes (or in other positions) it may not sound right and you could get other vibrations and notes. The same is true with the reed in the drone. There should be a notch or a marker at the base of the drone where it connects to the bag. On mine its a flattened area on on the pipe. The reed for the drone should always be inserted 90 degrees to the left of the notch. So if you hold the notched/flattened part up toward the ceiling the "flap" of the reed should be on the left.
Once you are inserting your reeds correctly you can start tuning. Tuning is done mostly by how high up the threads on the reed are. The threads should never be loose, but they should be workable enough, so as with some delicate effort you can shift them up or down. The higher you go on the reed, the higher the note. The lower you go on the reed, the lower the note. Since you have a gaida in D, you should tune to that. Take your right hand and cover the thumb hole with your right thumb. Your index finger on the small hole (the fleahole), your middle finger on the second hole and your ring finger on the third. This should give you a D when you play. I recommend downloading a tuner for a smart phone rather than buying one. I use Da Tuner Lite. It should what note I am playing and how far off I am from its true frequency.
Use the D fingering to tune that note first. Its your base note and it is also what the drone should be tuned to. Don't worry about tuning the drone for the time being. There are two other holes that usually need a little beeswax (its ok to use for tuning) or suet. The fleahole (the small one) and the last hole. To adjust the notes emitting from these holes place a little bit of wax or fat in the hole. More fat/wax makes the note lower. Less makes the note higher. The very last hole is used quite a bit for tuning. In you case It should play an "A" when all of the other holes but the last one closed.
Getting tired now. Will resume answering questions later. There are other guys in this forum that have alot more experience than I do. I hope what I have told you so far will help you maintain and start playing your instrument. Keep at it. Play atleast 15 minutes a day, or longer if you can. Don't let the gaida sit. Its like a woman, it can be different on any given day. But the more attention you pay to it, the more it will play nice for you.