Moderator here: Yes, suspensions can be cancelled.
Speaking in general, there is not a strict rule. For example, a suspension can be lifted if say, it's a first offence, it wasn't something that bad, and you know the user just had a bad moment... etc.
But note: this is not always true. While there is a set of regulations, not all mods act the same, since we're not robots, but we interpret the law case by case and decide the best solution for each situation.
How can one get a temporarily account suspension lifted before it ends?
I think one way would be to write to the Team and propose your case. Needless to say, your tone shouldn't be aggressive as that might leave your suspension at best and increase it at worst. Suspensions are not against the user, but towards the community. It's meant to isolate the problematic user from the rest of the community since we think that user is creating unease and problems on the site.
Wasn't that suspension set in place by a moderator?
Yes, suspensions are set by moderators (or the Team).
Can any other moderator just remove that suspension?
Only the per-site mods can and the Team obviously. If I suspend you on a site, a mod from a different site won't be able to lift it, since they're regular users on my site.
And why would it be removed?
Like I said above, if the case allows it, you can lift it. But there isn't a hard rule for this and it depends case by case.
Of course, if you get suspended by mistake, then your suspension is going to get lifted.