If I have a plugin installed, but am not using an element or workflow or anything to trigger the plugin, will it still affect performance?
It may affect performance depending on the exact plugin. Here is some insight from Josh on the topic:
Geoff | Top Shelf Templates
So, as a followup, can I uninstall a paid plugin, and later re-install it without having to re-buy it?
Hmm, not sure about that one. Might need input from @Bubble or others more experienced at adding removing plugins
Yes you can re install anytime, no cost.