Can a couple have a small wedding ceremony there?

Yes

No. Permits for weddings are obtainable for Carmel River State Beach, but are not permitted in the reserve. Point Lobos State Reserve is administered by CA state parks, but is a natural reserve, it's there to protect the natural resources.

Yes, but only if you guys invite me😉j/k

Yes, just communicate to park staff and have your details ironed out.

Yes. I don't see any problem there. You can inform the park staff and they should assist you.

You will likely be required to pay fees and perhaps obtain a permit. The park staff will be able to assist with that

I'm pretty sure

I would ask, i really don't know.

Probably but you might have to talk to park people!