... regarding mobile / app version. I don't play desktop, so can't speak for that version.
1. H2H matches: hole info beginning of a match should state the green speed. There's no other occasion where you play that you don't know what the green speeds will be. It's crucial to know the green speed when approaching, especially short approaches where roll comes into play. Why should this be a mystery when playing H2H holes?
2. H2H match stats: I'm sure there is a reason that stats are saved or posted for head to head matches, but I'm not sure why. I'm not sure why it would be considered as a turn-off among players, or why the H2H stats should be discrete. Stats could include: wins / losses (forget ties, they all resolve to wins/loss) and even forfeits, maybe a win/loss percentile; score count or averages (birdies / pars / bogey's, etc.); win / loss streaks, etc. I think overall, that would also cut down on forfeits.
3. Option to "Rematch" opponents (if both players agree). I imagine this is deterred to avoid potential issues with boosting, where people play themselves with multiple accounts, favoring one, major account over the other. But, the coins you win are pointless other than playing more H2H matches. It'd be a huge benefit to be able to rematch if you enjoyed a chat or close competition with a particular player... or just want to take you chances of settling the score (after a loss).