Should every IP address be reverse and forward resolvable?
You may not run into trouble, but it really is worth the fairly minimal effort to set it all up.
$GENERATE is your friend.
No there is no problem with that setup. If your machine connects to other machines it makes you "suspicious" but not more.
If the IP is used for outbound emails you will see a lot of trouble as not having a valid reverse DNS makes you look like a Spammer or Spambot. Or at least as an incompetent postmaster.
Non-server machines don't need PTR records at all, although if you happen to maintain an internally visible reverse DNS map for your own use that wouldn't hurt.
Making your desktop machines' names visible to the outside world might be considered a security risk, although it also falls squarely into the "security by obscurity" argument. That said, if you name your workstations after the employee that uses them then that information could be used for social engineering.
For IPv6 the IETF consensus appears to be that it's simply not worth the effort, particularly when using SLAAC which causes non-servers to pick random addresses and change them every so often.
Possibly, depending on the scenario.
Most likely
Not likely
There are very few cases where a PTR record is actually useful (such as for an outbound email server) but even then it' not a standardized requirement.