Not any. Some wallets has a different deviation path and you might have some trouble trying to change it to generate the correct addresses. Depends on what you're doing, generating a new wallet and getting a new seed can be a good idea at times, if you feel insecure reusing the seeds.
It's okay to switch wallets and get a new seed. Sending them when the fees are low would be better though.
This. Besides paying a transaction fee(which you should be paying a really low one), there's nothing really wrong with generating a new wallet(especially when moving from a mobile/desktop wallet to a hardware wallet). If anything, it's more recommended; just to be safe if it's the case that your wallet's keys have been leaked sometime in the past.