Use caulking to install a marble threshold

You can buy powdered marble dust which is used like a mortar to repair cracks.

The porosity of the tiles doesn't matter - the waterproofing happens on the layer below. You'll want to use something like Kerdi (the Kerdi shower pan kit is nice) or a similar product, or RedGuard, or another form of waterproofing.

The problem with marble is that it's a limestone type of stone, and susceptible to chemical attack. Over time it will lose it's gloss and go dull. How long this takes will depend greatly on your water and the products you use. It might only last a few years or it might outlast you. When it dulls you can either polish or replace.

JohnBridge.com is a tile forum, and the topic of marble showers has been discussed there. You might get some good info by browsing old topics. And John Bridge himself has a marble floor in his shower and wrote an article about it. He lists a recommended sealer and has some brief instructions on using it, too.