How much memory can a bot use?

Memory isn't restricted per bot like CPU, so you can use all you want. But if your bot uses way more than its share, people's clients will crash only on battles with your bot and you'll get a lot of complaints. :-) I'd say your bot should be able to battle itself without ever causing OutOfMemory errors.

Do Diamond/DrussGT get the same amount of skipped turns if you pit them against each other, or themselves? I've definitely seen some cumulative CPU load effect on skipped turns - eg, Diamond is less likely to skip turns against Sample Bots than against DrussGT. Some amount of skipped turns is not a huge deal. How many are being skipped? Your high memory usage could lead to increased garbage collection, which I think would count against your bot's CPU time, but that (a bot using a lot of CPU) can also cause a few skipped turns for the other bot in my experience.