I'm about to start tutoring with a teacher in Go. We're going to be doing similar things. My weekly homework includes:
1. 30 minutes of problems a day.
2. Play 5 rated games (i.e. games that COUNT with 30+mins on the clock for each player) and record game
3. Give a detailed review of my thoughts of 3 of those games
4. Memorize any professional game and, at the start of the weekly tutoring session, replay it from memory for my sensei.
But in a more informal setting here's what I'd recommend:
1. Immediately after finishing an in-person game, ask to review the game with your opponent from memory. Hopefully get a stronger player to watch you two reviewing the game, and maybe replay the game on a new board so that you can check the true board position to jog your memory.
2. Do problems! The Elementary Go series from Kisiedo is good, as is the "Graded Go problems for beginners" series.
