It can bog a system down. That is why font managers were invented. If you think you have too many fonts activated, open Font Book and disable the non-system fonts.
They can, but that is less of an issue now than it was in the past now with faster memory and usually more of it. I don't know what system you are using and how many fonts you have active, so that is all I can say on the topic.
The easiest way to find out if fonts are slowing you down is to go into Font Book and deactivate all non-system fonts. It should take less than ten seconds.