1) Definitely a problem. Should be fixed soon when all of the following are true: a) Mafia has mostly complete data about the new Hidden Temple, b) all the feature requests and bug reports about it, if any, have settled down to inactive, and iii) I'm going through that quest again with enough time to devote to scripting it. One or more of these may already be satisfied, but as any astute reader would probably have noted, iii is the biggie.
2) I have experienced this problem in my recent Axecore runs. In non-Axecore, so long as you had a wet stew before running the script (I always did), I never encountered this problem. Since I never encountered it before, I had roughly zero motivation to fix it. Now that I've encountered it more than once, the motivation is increasing.
3) I've never encountered this issue, but I'm also running BBB which has 100% run protection. All the script does is ensure you have the needed familiar available, then use the black market map. Mafia handles the rest, or so I assumed. I'd be interested to see some output where your familiar was not restored.
4) If this doesn't work, then it never has. I assumed originally most people would have the ballroom unlocked already. When someone asked if this script could also get the key, I simply added a line to attempt to get the ballroom key (all it does is set the key as a goal and auto-adventure), with a comment saying "does this work? no idea". You are the first person to provide feedback on the issue.
Today I worked on BatBrain. I'm often disappointed that working on one script means I'm not working on another one. Sigh. I'll try to get this one releasable again soon, but I'm about to dive into my second Kittycore attempt (first one had a rage-inducing misclick and was ruined AFTER THE SHADOW) so it might be a week or two before I get to this quest again, and in Kittycore I won't automate as much, but I'll make a point of testing this script while I'm there.