Learn English – the difference between “how long ago” and “when”

Both versions (with or without there) are perfectly normal things to ask. But if it is included, only the precise context (i.e. - what was said previously, who you're talking to, etc.) can tell us whether there refers to the location of the party, or the event itself.

Suppose, for example, you're talking to some friends in a pub, and one of them says "This is a really crazy place! Last week, two girls stripped off and danced naked on the tables!" It would be perfectly valid for you to say "Yeah! I was there! That was quite a night!"

The reason you can validly use there in that context is because essentially it can be applied to any place/time/event that's not here and now. Even though at the time of speaking, you're actually in the same location where the strippers danced, you're in a very different situation (they're not doing it now).

Contriving the situation even more, suppose instead, those two girls walk in and repeat the feat. You could say "That was crazy! I was here when they did that last week, too!".

In both cases you could use the other preposition. The "rules" aren't that fixed, and it very much depends on what you're emphasising out of different/same place/time/event. Not that I've ever been in either of those hypothetical contexts, but if I was I'd probably use there and here the way I've written it.

My reasoning would be that in the first case, both the time and the event are very different to "here and now". But in the second case the only thing that's different is the time, plus you've less reason to wish to emphasise the "not here and now" aspect of what you're talking about.

As regards "Are you there in the city?", you certainly wouldn't use there if you yourself were in the city at the time. Nor would you normally use it unless "the city" had already come up in the conversation. That's because in the city obviously refers to a spatial location that's not "here" (effectively, in that place, as opposed to in this place). It doesn't make sense to refer to that place if we don't know what place you're talking about, and it's confusing to have to wait for the words in the city to find out, so we don't generally phrase it like that. But if you had already mentioned the city, using there would be perfectly normal.

They do mean essentially the same thing, the up and off are mostly added for emphasis

Finishing off or up is generally used near the end of a fairly long task, or when specifically talking about the last portion of a task.

eg if I've got nearly a whole drink left, a friend is most likely to tell me

We'll finish our drinks, Jon, and get going

Whereas if I've got a couple of mouthfuls left he may say.

Finish your drink off, Jon, we're all waiting for you.

The latter both emphasizes the sentence (because my friends are waiting for me) and references the fact I'm nearly finished. The only real difference they apply is the emphasis - usually (but not always) requesting that the end of the task is expedited, or hinting that the task is taking too long.

They both tend to be added to long tasks, or tasks which are taking longer than normal, but this is by no means a rule. Similarly you'd tend not to add either to a short or quick task, as there's no need to emphasize... again, this isn't a rule, just a description of the most common usages.

Overall, off or up are virtually never necessary, they're colloquialisms added to informal speech. That said, they've made their way into formal speech too, and are fairly common.

If in doubt, you'll almost always be safe using "finish", but you'll also almost never be wrong adding "up" or "off" to the end.

(Note: the one caveat to this is that to "finish" someone would generally imply either killing them or knocking them out, if talking about a violent situation. "Finishing someone off", however, may imply something of an entirely different physical nature which I won't describe on StackExchange, but I'm sure you can guess...)