Use adhesive spray on the back side of it.
yeah why not??
In the auto industry, it is called the "head liner".
no
It sounds like the water drain hose for the sun/moon roof has come disconnected. There are 4 drains, one at each corner. You'll have to pull down the roof liner to get access to that corner and reattach the hose. If the hose is leaking and not disconnected, you can cheaply buy hose at the hardware store, and connectors and clamps to cut out the bad section and replace it with new. The other option which I don't know how to fix, is that the drain is backed up (clogged) farther down inside the car, and it's overflowing. That might need professional service.
To reattach the molding on the outside of your car you need to visit your local auto repair store. They will have some form of adhesive to help reattach the molding.
liner
Gain access by removing the roof liner. Check the cables to see if they have seized, replace them if they are. how do i remove the liner
A car that has no roof is merely roofless, but the name for such a car that has a retractable or removable roof is a convertible.
on the head liner on your car you will see a small cap near the dome light, turn it 90 deg and remove it, with the correct Allen wrench tun the bolt you see, that is directly connected to the sun roof motor.
The roof
I prefer an adhesive like PL300 or silicone for this. -If it has to be pulled tight you will have a problem, whatever you use.
no <><><> The first car did not have a roof at all.