When I first started I couldn't sit down with a tune in my head and pick out which keys to play. Now I can.
Couldn't play with 2 hands. Now I have an acceptable degree of 2 hand independence. But I find my cantabile-ness in the right goes down when using both. Right gets influenced by the left's rhythm. So that's is being worked on. Took a year and a half but it wasn't daily practice. Quite often it was in spurts.
So it can be done on your own at your own time and at your own pace without a live instructor. But I did find some paid online materials critical.
Piano Magic -
http://www.pianomagic.com/
here you will learn a strategy to approach playing with 2 hands. But conceptually it is geared for someone who wants to play, not play what they compose. Some of the concepts expounded are detrimental (seems to me) to composing but can be easily filtered out. If you do this course, just remember to have more respect for melody and its intricacies. I read about one thing he wrote about his experience of his students mistakes in pick out the notes. I saw how it applied to me and after that I could pick out notes in a long sequence. Ear training trains only picking out note 1 and 2.
For ear training, play the major scales cognitively. All 12 scales. Forget scales fingering for the moment. Use 1 finger. But you need to get yourself to the point where you can do all 12 scales in like under 2-3 minutes. Also dun make it a counting game, whole step whole step half step... . And dun be afraid to make a mistake. Just listen to how weird a mistake sounds. As for the other scales, unless you are the type that composes by improvisation, if the melody you hear is minor, you will switch to a minor scale automatically when pecking out the notes. If not, repeat the procedure for your next chosen scale.
As for a DAW, Reaper is the cheapest but has some of the best documentation like Reamix and community. I will not waddle into the question of whether it is the best but if you wonder why it is so cheap, well the developer made a lot of money when sold his previous project, Winamp. So don't worry about its quality. Way underpriced relative to others.
For other stuff, I found KVR forum has one of the best crowd with regards to music software matters.
So what left is to see if you what your really want to do with the keys, piano or synth.