Hey there!
I'm no expert, but I can try to help you out as best as I can!
First off, to answer the immediate questions:
The Avatar URL is just the URL of an image you want to use as your bot's profile pic. To get it, just Google whatever image you want to use, right click on an image, and hit "copy image address". Then, paste the result into the Avatar URL page.
The callback URL is a URL which GroupMe will send your messages to. So, any time you send a message, GroupMe will send a POST request to that URL.
Now, I know that might not seem super helpful; I first learned about web development using GroupMe bots, and I had a NIGHTMARE trying to learn everything on my own. I just had to get a really good example bot, and work backwards from there, taking it apart, figuring out all the parts, and so on. Unfortunately, the official example I REALLY like is fairly out-of-date now (it heavily recommends using Heroku, and they just dropped their free tier); however, one really talented GroupMe developer I know wrote
this example bot. It should be SUPER simple; you'll just need to install Node.JS (which you should be able to find guides for pretty easily), then use it to run that program. You'll also need to, like it says at the top, install and use a tool called Ngrok. That's just a little utility which will take care of all the port forwarding stuff for you, and give you a URL, which you can use as your Callback URL in that form.
I know from experience that this is going to be pretty hard, but once you get it working, it's the most satisfying thing ever. I think you'll really like it!
If you have any more specific questions, feel free to let me know. Like I said, I'm not an expert, but I honestly think I might be the only person who still checks this group semi-regularly.