Mankite. I am deeply struggling on how to answer this question without upsetting you.
Obviously or maybe not
the holes in the ceiling and their depth have nothing to d with anything. To the best of my knowledge no projector or projector mount comes with screws for attaching the projector or a projector mount to the ceiling. Mount manufacturers do not want the legal liability which would ensue if they supplied or even advised on how to safely mount their mount to the ceiling.
Most people use a ceiling flange plate to actually attach their mount to a ceiling. This is merly a female 1 1/2 NT pipe socket on a plate with four holes on the plate. Basically its called a pipe flange. You can buy one at home depot for about $4 or you can order facy ones from the projector mount companies with cover plates etc for about $30. But they all do the same thing. Hole spcings on the plate are about the same and the idea is to get one or two screws into a ceiling joist. Some plates are on sliders so you can can attach the piece that doesn't slide to a joist and then slide the actual pipe socket. You have to pick what type of screws etc to actually attach the flange to the ceiling. Then you have to procure them. One or two screws of the right length and type will do or you can knock your self out and use four but it is normally difficult to have all four hit a joist. In the old days when some projectors weighed 200 lbs, people opened their ceilings and added wood or used u channel to mount to studs and mounted their mounts to the u channel.
Next you need a piece of 1 1/2 NT threaded pipe. This attaches the mount to the ceiling and attaches or rather screws into a socket built into the mount. This pipe can be any length. It can be just a 2 inch piece having nothing but threads, it can have length between the threaded ends. It can be fancy, it can be adjustable. You can buy normal pipe at Home Depot, you can have then cut and thread whatever length you need. Short lengths are already made and they are called pipe nipples. You can join two pre mades into one by using a pipe collar found where the nipples are found. You can buy poles etc from the mount companies and pay a lot more.
Now you need a mount and yes in deed, these do come with screws for mounting the mount to the projector. The best way is to get a dedicated plate mount for your projector instead of a universal mount with spider legs. Chief makes several mounts. The RPA or the RPMA. What follows is the universal kit which is shipped with the mount or the dedicated plate. There are many plates and you must pick the right plate for your projector. So we have a RPA-U or something like that or a (RPMA-U) or an RPAXXX or RPMAXXX. Now to fill in the XXXs for your projector. Off to look it up in the Chief mount finder. Now back and its the 020. You can order just the 020 plate if you already have a RPA or RPMA with a universal or other plate. If you order just the plate you add some letters before the 020. SLB or SLM, something like that, I just don't remember.
Why don't you just give me a call later and I can walk you through all this and then you can order what you need frpom AV Science Sales. Craig is around today to help you.