I started from scratch at age 40 (I'm 54 now). I had played classical guitar and sung, but had no experience with the piano.
When I started I had no teacher and so I foolishly believed the Preface to Hanon, and started playing Hanon like mad. I'd alternate days between doing all of Part I of Hanon plus the major scales and arpeggios and Part II of Hanon and all the minor scales and arpeggios. I was working full time, so I practiced in the evenings about 1 1/2 hours, and it drove my wife and kids nuts (eventually I got a digital piano so I could use the headphones and spare them the pain). I also started working on two part inventions, some Scarlatti sonatas and some easy Schumann. I also scanned Beethoven Sonatas and the Well-Tempered Clavier for slow pieces.
Then after a few years I read Fundamentals of Piano Practice (C.C. Chang), and decided to ditch Hanon and just work on pieces. A lot of the suggestions in that book were useful to me, a lot of hands separate practice, thinking of notes in handfuls (parallel sets), finishing the daily work on each piece by playing through very slowly. My technique improved quite a bit, I lost my fear of "Allegro" and I got to the point where I could play a bunch of Mozart Sonatas, Schubert Impromptus, and some of the easier Preludes and Fugues from WTC. That went on for maybe 8 years. It was fun, but I never found a teacher who did more than say "Oops, you made some mistakes in there, better work on that bit."
Then over the past 3 years I've had two very good teachers who have been working on the basic technical things like posture, arm weight, tone production, and all that. That has helped a lot. Also, I retired and can practice 3-4 hours/ day, which is a wonderful luxury.
So, to answer your questions:
My practice routine now is to do scales and arpeggios in one major and one minor key and work around the circle of fifths changing keys every two days. So I get through the whole circle of fifths every 3 1/2 weeks. Since my teacher always has some suggestions about general technique, I use the scales and arps as a substrate to try out the ideas. Then I work on Alberti bass patterns for the LH and do the trill exercises from Hanon. That takes me 30-40 minutes.
Then I work on pieces. I start hands separate and work until I can play each hand quite fast (as you do). I also play the new pieces for my teacher right away; I don't aim to impress her, but letting her see how I am starting to work lets her correct any early problems that might get engrained if I waited until I felt ready to perform the piece for her. She'll usually have lots of suggestions for better motions to make the parts easier or to produce better sound, so that gives me specific things to work on. I might spend 20-30 minutes on a given piece, and I always break it down into bits small enough that I feel like I've accomplished something in that time (as you do, too, I think).
For pieces that are farther along, where I've got them memorized, I might spend 20-30 minutes trying to get a sound I like on just a few bars. So this week, for example, I worked a lot on the first six notes of Brahms Intermezzo 117/3, triple octaves, trying to get the voicing, volume, and phrasing the way I like them, and figuring that if I solve that, the solution will spread throughout the rest of the piece.
I'm working on six pieces at the moment, so that takes me to 3-4 hours most days, but if I had less time I'd use the same approach, just working on fewer pieces.
I try not to get too routine - for example I don't work through pieces in chronological order, Baroque, Classical, Romantic, everyday. If I'm really interested in one piece or the teacher made an interesting suggestion, I might break the routine and spend a couple of hours working on just one piece.
Between several pieces and the technical stuff, there's enough variety that I always find it interesting and enjoyable. If you love it, even as an adult beginner you can get to the point where you can play great, serious music. It's definitely worth the struggle.
Bill