1. How long to connect at Dub?
There is a BA flight that gets in 2hrs 50 before the EI flight goes.
Would this be ok?

Yes. This should be plenty of time.

Note that your BA flight will arrive DUB T1 and your Aer Lingus flight will depart DUB T2. If you have bags and/or need a boarding pass you will need to use the covered walkway. 10 min. If you don't, you can clear security in T1 and walk to the T2 gates.


2. Would I be able to check in for both flights in London?

No. Note also that BA won't interline bags to Aer Lingus on separate tickets.


3. Would the answers to 1 and 2 be different if we went with EI from London to Dub?

This would seem a better strategy. EI are good at through checking and may even provide you with lounge access in LHR if you have a EI J boarding pass on hand. EDIT: as a BA silver you get this anyway.

Connection at DUB with bags would be much easier.

But if you have no bags and can print your Aer Lingus boarding pass online, the transfer T1 to T2 id almost as easy as T1-T1.