Hole size allowed in 2 X 8 joist

I am adding a shower on the 2d floor. It is 42" square. The floor is 2 layers of 1/2" plywood. Below the plywood are joist that run a 11 foot span. Moving from the center of the shower towards the outside of the rectangle of the shower there is a 2" x 8" double lam joist 1/2" and 3 1/2 " on center, and then there is a wood 2" x 8" joist 14" from the shower center. None of those joist will have any drain holes through the joist, so my guess is that I do not have to add anything on that half of the shower area. Am I right?

However, moving from the center of the shower the other way, there are two wood 2" x 8" joist, 2" and 18" on center from the center of the shower. The one at 18" o.c. must be drilled with one 2 1/2" hole for the shower drain. My other question, is it ok for that hole to be in that joist? Where can I find information about what are allowable holes in joist?

It depends, slightly on where you live.

In some places, the hole can be 1/3 of the joist depth (actual measurement, not nominal size); others, only 1/4 of the joist depth. In all places, it CAN NOT be within 2" of the top or bottom of the joist.