Authenticating Very Short (Sub-Block) Data If I'm encrypting very short/small data - like an int or a long (32 or 64 bits), does it make any sense to authenticate the ciphertext, when using an "online" mode of operation (like EAX)? 

Essentially, guessing the plain text would (assuming no weaknesses in either the encryption or the authentication) be easier than forging the authentication tag if the plain text is shorter than the block size of the cipher - or equally hard if truncating the tag to the same length as the data when using EAX. 

Are there any scenarios in which tags longer than the data would be useful? (Or are there any actual research results on this?)

Does any of this change if the key with which the individual ints are encrypted changes?
First, the fact that the data is "easy" to guess (in the sense that an attacker has a one-in-2^32 or a one-in-2^64 chance of guessing correctly) doesn't mean much if the attacker has no way of checking if his guess is correct. Or at least, it's not a problem with the cryptography.

Second, even if he does have that ability, the problem of protecting your data's secrecy is separate from the problem of protecting its authenticity. For example, it might be bad if an attacker can deduce that a message says "Yes", but it might be even worse if he can then tamper with the message so it now says "No". 

In this example, the message itself was effectively only one bit long, but it definitely would make sense to have a long (e.g., 128 bit) authentication tag!

To answer your final question: No. As long as each key is random, then periodically changing your key is not a problem. In fact, in many situations it's recommended in order to limit how much data gets compromised if an attacker manages to obtain the current key.