FYI, regarding the last video, here are standard amounts that you should expect to receive for selling to friendly AI (if they are truly friendly, not pseudo-friendly):
Open borders - 50 gold
Lux resource - 240 gold
Strategic resource - 45 gold
If some of the payment is in gold/turn then it decreases slightly, e.g.,
Open borders - 1 gold/turn (30 turns) + 19 gold
Lux resource - 7 gold/turn (30 turns) + 20 gold
etc.
For Research Agreements, if you are an era ahead (e.g., in Renaissance when they are still in Medieval) then expect to pay the standard cost + 100 gold.
In your deal with Elizabeth, the reason she changed her money offer was because she also added in her open borders.
You should be ok now that you have some longswords, but a few more siege would have made it so much easier.