Culture production structures do stack, yes.
Don't send caps out alone--keep a good number of frigates with them, and don't forget about upgrades either.
There are a couple of 1v1 maps that have a larger number of planets than the tiny 'duel' maps. If you browse through them in the list, it will tell you how many planets each has, so you can estimate how long a game would take on them.
False Belief Monitoring and Eyes of the Converted don't give any spread bonus, but they're a branch off the culture line, rather than the end.