Finland holds the record, submitted their application in March 1992 and became member 1st of January 1995. Norway would've been even faster but their referendum failed.

If I'm not mistaken then Turkey holds the record for taking the longest, they were given official candidate status in 1999 and still haven't joined. Aren't anywhere close to joining because they're not implementing the necessary legal changes etc.

Finland didn't have much to do they were basically ready before they applied, while Ukraine is currently working through the accession chapters at breakneck speed, not wasting a single parliament session. Early 2022 they were so fast the EU Commission couldn't keep up with double-checking. Still, there's a lot to do.

I was under the impression a country could not join if they are in a conflict? Am I wrong here, is Moldova in a conflict now.

I'm not aware of any legal barriers to that, I think it's a political question. Russia being advised that if it's not out of Ukraine by a certain date the last thing her soldiers will see is Eurofighters tearing through the sky would presumably make Putin shit bricks.

Moldova very much is in a conflict, Russia has been propping up a puppet regime in Transistria since the early 90s.