1) I am not sure because I haven't tried that before. I have tried getting a CX award with BA miles and I could NOT use AA as a connecting flight to a CX gateway.
2) From personal experience not too difficult when compared to getting awards on US carriers. Sometimes, I have asked the US EC to send a message to London to see whether they could release a seat for an award. When I do ask I make sure that there are plenty of seats still left in First. On other occasions, I needed to take 2 BA flights to reach my destination and sometimes 1 of the 2 flights is not available so EC will send a message to London to get a seat released.
3) Yes, you can book the ticket and do NOT need any certificates. The only award that I know of right now that needs a certificate is for upgrades.