1. How do I use my light ships most effectively?
Should I use them in one large bulk in one trade node or split them up to the nodes I located my merchants? That is under peace, so no "bigger fleets are safer" considerations.
It seems that watching my income after testing a few variants, the "one big fleet protecting the home node" works best. Is this true?
It is, I think, better to use your ships to patrol nodes feeding into your home node. Having ships protect trade adds their trade power to your total trade power in that node; this is multiplied by the maximum trade power modifier (just like trade power from provinces is). If you have a merchant directing trade to your home node, you redirect your share of trade power (now additionally increased by your trade efficiency) to your home node. If you have a merchant collecting in your home node, you collect money based on your share of the trade power in that node (again modified by your trade efficiency).
This means that steered trade benefits twice from your trade efficiency, which means adding power to trade nodes you're steering trade in is more efficient that adding it to nodes you're collecting in. There doesn't seem to be a great reason to use more than one trade fleet; just park your light ships as far upstream in your trade network as you can and let compound trade efficiency do its magic.
I could, however, be missing something entirely.