It's 5 years since I've been so info is a bit dated.

1) IMO 2-3 full days in Havana is sufficient. It's quite small and there isn't that much to see. Then I would hire a car and head out into the real Cuba. Driving is very easy with little traffic on the road but signposting can be poor.
You can go west to Pinar del Rio, Vinales Valley and the tobacco growing regions. Nice scenery and really a step back in time. Food was an ordeal though.
Alternatively head east to Cienfuegos, Trinidad and the Bay of Pigs. Cienfuegos is a nice clean city with much better food options. Trinidad is a little overrated and the Bay of Pigs is more just to say you've been there. Apart from a little museum there isn't much to see.
Read the guideand take your pick of whether east or west appeals more. Both could be done in a week but it would be quite rushed,
2) Yes one in Havana and one in Cienfuegos. PM me if need be.
3) I would go for the Havana Libre as a safe mid range option. It's nice and central.
4) I've no idea. It's not how I'd want to head to Jamaica but may be safer than Cubana. Personally I'd just take Air Jamaica.

5) Tips
-I used the Fodors guide which I found to be nice and brief. Ideal for a week IMO.
-Make you sure you sample a mojito and a cuba libre.
-Finding decent food can be hard in Cuba and particularly for a week or so. Finding vegetarian options won't help but you can live on rice, beans and fruit. I can recommend a nice private restaurant to eat in. Also Chinatown may provide you with a value alternative.
-Shop around before renting a car.
-Don't run low on petrol in Trinidad, not a lot of garages there.
-If buying rum the local $ shop is a good bet. Not sure if Castro has changed the system for buying "luxuty" goods.
-Don't buy cigars off the street touts. A well connected casa particular owner might be a good bet if the airport/hotel shops look pricey.
-Don't listen to the Buena Vista Social Club CD before going as you'll hear it played a lot when you're there.