It is better to use a different passphrase for each key but it is also less convenient unless you're using a password manager (personally, I'm using KeePass)
> - How much less secure is it to not use a passphrase on a key?
That depends on the security of the computer where the keys are. I remember a Firefox vulnerability where one site exploiting it was looking for ssh keys on the local file system. So I'd say that a passphrase is very important.
> - Should you use a different key per user account, per server, or per use-case (i.e. personal or work)?
Personally I'm using a key per account per host.
> - Does increasing the amount of bits in a key really have an effect on the security of the key, or does it not make much difference in a real-world use?
Yes up until 2048 where the returns of increasing the amount of bits will start diminishing.[1]
[1]: https://www.gnupg.org/faq/gnupg-faq.html#no_default_of_rsa4096