Imagine that a government seizes a large amount of bitcoins in a raid such as with "Silk Road". Is it possible to invalidate those particular coins and send them back to the "pool" to be re-mined so that that government cannot profit from the seizure?
Technically, yes it's possible to do this. Practically, doing this would probably break everyone's trust in Bitcoin.
One of Bitcoin's principle guarantees is that nobody can confiscate anyone else's bitcoins through the Bitcoin protocol. This protects all of us, but it also means that we're each responsible for keeping our private keys secure. If we fail to do that and someone---like a hacker or government agent---steals our private keys, then they also get the benefit of Bitcoin's confiscation resistance.
If we weaken this guarantee even once to confiscate bitcoins from the person or group we like the least, then it becomes clear that Bitcoins aren't secured by math, they're secured (or not) by the same sort of social guarantees that secure bank deposits.
If you or anyone else personally wants to prevent your bitcoins from falling into the wrong hands, you can use simple encryption software or Bitcoin multisig to try to prevent anyone from getting your private keys. Doing this in a way that is secure against rubber-hose cryptanalysis is hard, but better tools for it may become available over time.
Using locktime transactions or the upcoming OP_CLTV opcode, you can even voluntarily choose to give your bitcoins to future miners if you have to delete your keys to prevent an attacker from seizing them.
No, once they are mined they are around forever. If someone was able to delete the wallet file (and any backups) they could essentially make the coins lost though, essentially making it impossible for anyone to ever spend them.
A transaction fee could possibly be thought of as re-mining the coins since the miners will get payment of those coins again once the block with that transaction is mined. This is kind of a silly way of thinking of it though.