Is it better to use a different passphrase on each key, or does using the same one not matter much?
If the keys are for the same thing (i.e. your personal `id_rsa` and `id_ed25519`), then I'd personally be comfortable with the same passphrase. Different passphrases should be used for different purposes (e.g. you shouldn't use your personal passphrase on work-specific keys).
How much less secure is it to not use a passphrase on a key?
Depends on the situation. I personally err on the side of caution and use a passphrase on all keys unless it's not physically possible.
If you expect to be moving your SSH keys across machines (e.g. to use your same personal key on both your laptop and your desktop), then they should absolutely be passphrase-protected, even if they're only transferred via encrypted media.
Should you use a different key per user account, per server, or per use-case (i.e. personal or work)?
There's not really a right or wrong answer to this besides "don't reuse the same key everywhere". I personally maintain one key (really two: one RSA, one ED25519) for all of my personal devices, and maintain a strict policy of full-disk encryption on such devices. I've occasionally maintained separate work keys so that I'm not ever in a position where I need to make my personal keys available to an employer.
Meanwhile, for situations where a server needs to connect to another machine via SSH, each such server gets its own key. That way, if a server is compromised or decommissioned, I can revoke access by key.
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?
It makes a significant difference. More bits → exponentially more attempts required to brute-force it.
How/Where should private keys be stored on a device using them?
Depends on the device.
A reasonable balance between security and practicality is for any portable media (including portable devices, like laptops/tablets/phones) to be encrypted (in addition to the key itself being passphrase-protected). Better security would be to extend this to non-portable media and machines as well (but this is painful to enforce on servers unless you have physical access).
The directory in which keys are stored should only be accessible to the OS user actually using those keys (so, for example, `~/.ssh` should have permissions `drwx------` when viewing with `ls -la`).
Basically, server SSH keys should be treated like you'd treat your SSL/TLS keys.
What are some of the pros and cons from a security standpoint
...of?
and how may doing different things affect the usability of a key?
Pretty much everything involves security v. convenience tradeoffs. Generally, the more secure, the less convenient, and vice versa. While absolute security is ideal, a lack of convenience makes it more difficult to effectively enforce (e.g. as part of a company-wide security policy) unless you're willing to put in the work to build up an effective workflow around it.