A couple of things to add to Gardyloo's comprehensive post.

Itn 1 Q1. Use the AY codeshare on the ARN - LHR leg to get the cheapest price. The taxes almost halved in my case.

General Qs. Q1. There is an option to save itineraries to your OW profile, but you need to register on the OW website. I haven't used this but I suspect this means it is stored on a OW database and can be retrieved from any computer.

Q5. I have found that the miles earned seems to be dependant on the FF program. For example a BA flight LHR-HKG pushing miles to BA earns a different number of miles than when pushing the miles to AA. From my experience I have not found that Great Circle Mapper and Mileage Monkey do not accurately reflect the miles you will earn on AA. However both seem to be within 20 or so miles usually, if not spot on. I haven't tried milecalc.