About inbox rules:
They should never ever switch order. If you can reproduce this reliably, let me know and I'll file a bug. However, by default, inbox rules are created with an additional predicate of "stop processing more rules." This keeps more than one rule from processing any single message (*normally* this is a good thing).
If you want multiple rules to process in order, then make sure "stop processing more rules" is not checked on those rules.
Also, I just tested this running Firefox only on my test Outlook.com account. We're committed to supporting a wide range of common browsers across platforms--not just IE/Windows.