I should preface this post by saying I don't own a Mini and I haven't fully read the literature on them. But this is what I've gathered through conversations and light internet reading.
So, to answer both of your questions;
Once you open the case, you've voided the warranty. It can be done fairly easily, and if you're careful they might not know you did it, but it technically voids the warranty. To keep it under warranty, you'd need to send it to Apple, or bring it into an Apple store where they'll do it for you.
BUT, and this will tempt you to open that sucker, the ram is on a stick, not soldered to the motherboard. Which means, if you don't care about the warranty or you'd like to try to 'get away with it,' you can replace the ram yourself with a larger stick and be on your merry way.
If the issue is "I'm not going to pay Apple-RAM prices when I can PriceWatch it much cheaper!" it's possible that an Apple tech at a store will install it for you if you walk in with the RAM in hand already. This I am absolutely NOT sure of, and I can't say I've ever asked an Apple guy to install a third-party piece of hardware.
But if the issue is more of a "well, putting that extra ram in it really stretches my budget right now," then I'd say try to stretch your budget (or wait for a windfall) and have Apple send you the Mini with 512 MB in it to start with. Believe me, you'll enjoy your Tiger experience a LOT more with 512.
Hope that all helps,
-rand()