Answers:
1. Yes. Not likely from an encounter 1 week earlier. Usual duration is 3-8 months or more.
2. Yes, it is possible from any encounter you had. Someone who has it but not showing warts has more chance to infect you. The one who had unsafe sex with you was also a high risk.
3. Don't self diagnose. If it doesn't go away in a few weeks, see a doctor.
4. No cigs, no or little booze, more sleep, more exercise, eat healthy, take vitamins that boost immune system, less stress, stay away from people who have colds, take the flu vaccine, etc.
5. You can assume you have the same strains (most sexually active people have multiple strains) as he has. You cannot re-infect each other and he is the only partner you can have sex with (safe or unsafe) and not worry about infecting that person or getting a new strain.