Negative, unless they lose it.
You can only annex a) one-province countries, or b) pagan countries. Hence why pagans are something everyone shoots for.
You can only send missionaries to provinces you control, by clicking on them and clicking "Send" on the missionary button that appears next to the city screen.
In Vista(or at least mine), it's Users > (Your name) > AppData > Local > Virtual Store > Program Files > Paradox Interactive > Europa Universalis 3 > Screenshots
Galleys will be blown away. Use only big ships to cross the ocean. How many is up to you, though a few is wise and it allows you to keep exploring/recover if any are lost to attrition.
How soon you should get the idea depends on your strategy. If you're a strong militarist, you should be more focused on stability, religious and army-related ideas. If you're a trader/pacifist, you should be more focused on acquiring commercial ideas and, of course, Quest for the New World, which will help any commercial power enormously.