Replacing a bottom bracket cartridge with:

https://www.amazon.com/Shimano-Squar.../dp/B0068FVOEM

Taking the old cartridge out it was heavily covered in grease(1/8 inch thick) on the cartridge surface. I assume this was done for corrosion protection. This is the first time I have every taken a bottom bracket out, so looking inside the bottom bracket shell I see that the chain stay tubes and seat stay are open into the bottom bracket shell. And I have holes in the ends of the chain stay tubes, so water could get into the tubes and travel down to the shell. I want to caulk these holes closed, but maybe this would make it worst for corrosion in the shell(No air circulation). Thoughts on this please?

Second, I am trying to decide what to use, grease or anti-seize on the threads of the bottom bracket. I am trying to make sure of no clicks/creaks, which I had in the old cartridge. If I used anti-seize on the threads then I would grease the bottom bracket area inside the shell. If I just use grease then I would just use that on the threads and inside the shell. I might be over thinking this, but I hate noise in the drive train.

Finally on what grease/anti-seize to use? I have Park grease and Finish Line Teflon grease(white) on hand. For anti-seize I have a jar of auto Permatex anti-seize for aluminum.