I'm not familiar with any free software that's available but you can get a free trial for 30 days of HEM2 which I would highly recommend.

As far as hours of play goes, play as much as you can if its something your enjoying! Forget about the monetary value that you're playing for and focus on them in terms of BB's of BI's. Winning $10 isn't hugely exciting but winning 5 buy ins is awesome for any limit! That would be the best advice I can give you for trying to maintain your focus of your playing for money that isn't meaningful to you.

Firstly, if you're struggling to keep your attention fixed playing the lowest stakes just remember that your win rate will be so much higher that your hourly rate for building your bankroll will still be okay.

There also won't be much difference in the learning experience between 2NL and 10NL, at this stage it's all about getting in as much volume as you can, and becoming comfortable with your pre flop ranges and standard post flop spots.

As for a database, there's a free trial for HM2 and PT4 which will keep you going for two months, so at least use that.

Lastly, if you're already picking up on problems with non technical aspects of your game, I would heavily recommend that you read The Mental Game of Poker by Jared Tendler. Learning the stuff he teaches when you're at the beginning of your poker journey will help enormously.