... Research Level
... Population Size
I have had a quick look through the forum and FAQ and couldn't find an answer (or at least one I understood)
Does the first one mean the current +Research Rating, or the current absolute total value of Research ?
Which cards talk about "Research Level"? I don't recognize that term. There are cards that talk about the level of your labs (meaning 1, 2, or 3), but I think the term you're looking for with this question is Research Rating. And that is your research-per-turn figure. I can't think of any Event cards that care how many light bulbs you have accumulated.
Is the second the count of all my yellow markers on the different buildings, available workers, happiness markers, military units?
Yes, if by "happiness markers" you mean "discontent workers." Your population is all the yellow beads that have made it out of your yellow bank (and are still out).
Also, I am assuming my understanding of 'civilisation strength' when it comes to other events and aggressions means my Military Strength?