As you suspected, the answer to the first question is "of course it's possible". The question is always how much time it will take.
And that question is not answerable. Everyone is different, everyone learns at different rates. The fact that you are some particular age or that you have no previous experience doesn't matter: everyone was 15 once; everyone started learning their first instrument once.
Generally, you will find that it will require longer, perhaps even MUCH longer to do this SOLELY with self-study. If you have monetary reasons for not having a teacher, try studying under a teacher for a while just to get started in the right, then see the teacher at wider intervals later. I recommend finding a teacher and talking to him/her about it. (If the teacher you find isn't interested in working with your issues, find another teacher.)
IMO (I don't have humble ones!), the best way to answer this question is to advise you to forget your end target, at least set it aside and pay it little attention.
Instead, pay attention to the trip to get there. Perhaps you'll never reach the point of being able to play these two pieces the way you envision; perhaps you'll get better! But no matter what, you'll work your ASS OFF along the way.
Oh, you'll have lots of fun along the way too :-)
The old saying about the journey of a 1,000 miles starting with a single step is true.