Am i safe?

Safe? From drops of water? No. Safe? From the roof collapsing? Most likely yes.

Would I be OK with this if I were you? Oh hell no.

Is there some kind of Housing Dept in your area?

No

A failure is likely in the coming days, weeks, or months. I would not dwell here or leave valuables here.

As a landlord and a roofer..... Your landlord is a moron and deserves the insane bill he's about to get to fix it.

That is..

After he tries to cheap out 6 more times lol.

Would have been so much cheaper just to do the flashing proper, or, if gonna do a new roof, to actually do a new one not an overlay, esp with metal. But dumb is gonna dumb

Is water still coming in?

Previously wet ares and the insulation should dry out in time. Depending on how much water they got, some areas may be loose, so don't go poking at them.

Sorry you have to deal with a cheap landlord, OP.

You should be okay, no catastrophe about to happen.

Personally I’d stand under it and push it up and down a little for a bit till it fell. Once I’m covered in dust and the rooms destroyed I’d bump my head. Then I’d call an ambulance for a concussion. Then I’d sue the landlord. I’m just an idiot roofer though so don’t pay me no mind.

Make sure you keep paper (digital or physical) records of your interactions about this issue. Just in case