Hi Mariusz,
Short answer - Hack something together in the fastest way possible, don't worry about it being clean, tidy or even tested. Because if you do, you'll still be working on this project in 2 years time... Look at using something like PhoneGap [8], just enjoy the experience and ship it :)
If you genuinely want to start learning this stuff, you need to ask yourself what it is you want to work on? Do you want to do backend (e.g. all the server stuff, nothing visual), or do you want to do frontend (all the visual/pretty stuff the user sees), or both? Are you doing this for immediate financial gain [7], or a spiritual journey of self discovery and learning [6]? The world of web dev is changing almost every couple of months, stay on top of your game by reading blog articles from other developers and keeping on top of tech new. Personally I use Feedly [9] to aggregate these feeds into one place. Consider getting an internship somewhere with other good programmers, learning from inspirational people will speed up your personal development massively (I wish someone had told me this 8 years ago).
Long answer;
Responsive/adaptive design does not necessarily make a good mobile experience, and rarely will you find a mobile app which has the same workflow as the website. Ideally you need to storyboard each experience and wireframe the UX accordingly. Likewise with the UI, colors and sizes which work well on desktop often won't work very well on mobile/tablet (especially if you are designing your desktop site mostly towards PC users, due to the variations in color display).
There are tools out there now which allow you to package up your HTML/JS/CSS/images into a native application bundle, meaning you don't have to learn how to write native applications. There are a whole bunch of these products out there [1], but most of them suck, here's why. Building a client side JS application is *hard*, you have to understand the different JS design patterns in order to write clean and stable code, whilst understanding the importance of unit testing [3] and real browser testing [4]. You also have to understand the impact of latency, if you don't compile your assets into a local bundle (instead opting to just wrap a browser window in an IOS app), then your app experience will lag between clicks (because each click is a page load). To get around this you need to build your client side app to be completely independent of the server side, which includes maintaining a view state (e.g. changing/rendering the display upon changes being made). Other libraries exist for doing this such as Ember [5] and others, but they are still quite alpha and have performance concerns too. Also in regards to bundling, there are very few tools out there which will automate this entire process, for example creating a spritesheet of UI images so you don't have to make multiple HTTP asset requests, or embedding the images as base64 in your stylesheet (although that has render performance concerns).
Then you also have the API, building a clean RESTful api is difficult and in actual fact may be the wrong approach for your mobile app.. why? Because each API call has a lot of overhead, and this usually results in UI latency if the user has poor signal. There is some work being done to use websockets instead of ajax calls, but this starts to get into quite deep territory.
Gonna cut this short, as I try to limit myself to 30 minutes on any given reply. Again don't worry too much about what I've put in the long answer, that's just there to give you some insight into the things you'll start thinking about as you get deeper into your journey.
Hope this helps dude
Cal
[1] Google search for "app maker iphone"