This has frustrated me for a while, and have been unable to find answers. Why are none of my resource nodes giving me the full +1 as they say? Instead when I hover over how many of that resource I have, it says my income is 3.8, when I have 5 nodes! What is causing this reduced output?

It's probably because you're playing on slow game speed as resource income is 0.75 per node and is rounded up so 5x0.75=3.75 rounded to 3.8. This is because resource income is also dependant on game speed.

isn't there also an winter effect that reduces in come from strategic resources?