1. Well, there is no way to accurately predict how long it will take them, but you can use your criteria and factor in the "Cost Factor". On Monarch level, the cost factor is 9. That means something that takes you 10 shields to build will take them 9. A tech that requires 100 beakers will only require them 90 beakers. However, since the AI isn't as smart as a human, when figuring out tech research rates, I would add ~5-10% to the cost factory (making Monarch 9.5 - 10). They just aren't as smart when it comes to building the right improvements, and limiting their military. So a Monarch level AI might research that tech in about the same time as you (at the most).
2. It depends. If the rich AI has an important tech, I would go for the tech right away before your tech's value goes lower as you sell it around. Money can't do much, techs can do a whole lot more. You can then sell your tech and the AI's tech you aquired for even more gold than you would get. It's just trading to maximize your benefits.
2. It depends. If the rich AI has an important tech, I would go for the tech right away before your tech's value goes lower as you sell it around. Money can't do much, techs can do a whole lot more. You can then sell your tech and the AI's tech you aquired for even more gold than you would get. It's just trading to maximize your benefits.