Based on those requirements I'd fly into City (much quicker arrivals, less chance of chaos at immigration) and out of LHR (more direct transport via tube/HEX).
1. I would aim to be on a train no less than 1:10 before my flight. Security is close to the gate but AMS involves a lot of walking.
2. 17:30 by Jubilee then DLR
3. Pass - annecdotally both have let me down from time to time.
4. LCY is the more painless to use but I'd also bear in mind risk of fog (albeit March isn't too bad in that regard).