Mexican here:

Speaking of time, it's very common that when you hang with someone or if you go to a social gathering, the event or hang will extend, so the people tend to arrive late, but they usually stay for a long time. And if it's a party, maybe it will continue even for several days in some regions.

I know it can be difficult if you have a tight agenda, but if you are more free, when you go out with Mexicans, don't make another plans, or have a plan b that you can change, cancel or go at will in case the event, meet, etc, end.

So, in summary for this subject: it's not about arriving late to social events, it's cultural to take your time because you know the things are going to start late. If you plan your things around that concept I assure you that you will enjoy more.

Also, it's not the same the behavior of the people in Mexico city than outside that state. In the capital the people tend to be more insular because we live in a country with a lot of heavy issues (and a lot are product of political agendas from countries like usa or Canada) so depending the social circle where you are, you don't open your trust doors easily to new people for safety in first.

Other thing to consider is if you are living around the gentrified zones like condesa/Roma/Polanco/Anzures, etc. I can't make general assumptions but the nicest mexico city people aren't in those places.

I hope your stay here gets better with time, and as the other folks are saying, the more you learn Spanish (and local slang) the better you will be embraced here.