What size drill bit do I use for the holds?

I don’t recall the size of this screw. However, what you want is the determine the minor diameter. The major diameter is the diameter to the outside of the thread. The minor diameter is the diameter of the screw WITHOUT the threads, just the central shaft. This would be the diameter of the required hole if you are drilling, say into the grout line.

Will this product rust?

Brass and Chrome does not rust. (Only iron and steel rust.) I have had ours installed for 2-3 years with no problem. This is a commercial unit which I have seen in major hotels without issue.

What are the dimensions

The dmensions of this were something I tried to find all over the internet to no avail, so I chanced it and ordered three since they are solid brass. Soooo glad I did! They are super sturdy and the perfect size. These are the triangular corner shower caddies, not the wire one that shows in some of the Amazon photos. DIMENSIONS: 9-3/4" at the widest point of the triangle and 6-3/4" deep. The lip around the three sides is 1" high. The slits to let water drain are small enough that your razor and other stuff will not fall through and are positioned perfectly to let all water drain fully. This caddy is bigger than the "soapdish" size noted in the description. It will hold 4-5 average size 16 oz. bottles of shampoo/conditioner or 3 larger 20+ oz. bottles. So it is not humongous and not small. I read here that someone else installed an extra one upside-down and lower to rest one's foot to easily shave legs. The underside is smooth with no edges, so it is perfect for this!

Where is the product manufactured? Thanks.

This high quality part appears to be made in China. From their website, http://www.sanliv.com/about, they show what appears to be a factory truck that is Chinese. Since I bought this part earlier, I have been aware of seeing it in a number of higher-end hotels. It is made to last and I highly recommend it.