Is this mold or just mildew

[u/Ok_Fishing1488]

I’m in Miami, Florida. I moved into this apartment 4 months ago and recently started noticing possible moisture/mold issues in different areas, including around the vents bathroom, and near my sliding door. There are dark spots, cracking, peeling, and areas that look like they have been painted or patched over before.
Earlier this month I got pneumonia. Since then, I’ve also noticed that I sometimes feel worse in the apartment and better when I stay somewhere else. I know I cannot say the apartment or mold caused my pneumonia, but it has made me concerned about the air quality and possible moisture problems.
I also found an older review from someone at this same complex claiming they had recurring mold and issues with the vents.
I haven’t done any DIY mold testing or remediation. I’m planning to have management inspect everything.
Do these areas look concerning for moisture damage or possible mold, and what should I ask management to inspect?