To expand on what Kulgan said:

You can find technology costs here. You will see that plug bayonets costs 30 RP while other early game techs (Common Land Enclosures, Empiricism, etc.) cost in the 31-37 RP range.

An observatory affects global research rate. Whether it is really 4% as the in-game help says or 10% as building_effects_junction says is presently unknown.

There is absolutely no evidence adding more Gentlemen yields diminishing returns in terms of RP/turn. A trait-less, ancillary-less 3-star Gentlemen will add 3 RP/turn to a particular college, period. They just appear to add diminishing returns because the majority of RP comes from universities.

Let's take Empiricism for example. It costs 31 RP. A 9 RP school will research it in ceil(31/9) = 4 turns. Adding a clean 3-star Gentleman will reduce that to ceil(31/(9+3)) = 3 turns. But to get it to two turns, you will need two more 3-Star Gentlemen: ceil(31/(9+3*2)) = 3 turns; ceil(31/(9+3*3)) = 2 turns. As you can see, while adding extra Gentlemen did not reduce their individual contributions, their effect on turns-to-completion diminished. But that is not to say adding extra Gentlemen necessarily yields diminishing returns; consider the next example:

Let's consider Social Contract, which costs 45 RP. With just a 9 RP school, it takes 5 turns to research. With 1 3-star Gentleman, 4 turns. With 2, 3 turns. With 3, 3 turns. As you can see, up until the 3rd Gentleman, adding more Gentlemen had a significant effect on turns-to-completion. In our Empiricism example, it was only up to the 2nd Gentleman.

This also means that traits such as "Scholar" have a minuscule effect on turns-to-completion in the mid/late game; Classical Economics for example costs 436 RP. It would be unlikely that 1 extra RP/turn will make much of a difference in terms of turns-to-completion in this case.