The answer for all your questions is "it depends."
1. It depends on the area you live in. In many areas of the US, BSN is becoming the preferred degree for nurses. I expect that this will only increase in the next few years, so if you live in an area where there are a lot nursing schools and competition for nurses, it might make it harder for you to get hired with just an ADN. I'd personally recommend going right for your BSN for a few reasons. One, it's easier to get hired. Two, you have more opportunity to move into management positions. Three, you have more time in school to become prepared for NCLEX and your first job. Four, it's really hard to be in nursing school while you are working 12 hour shifts as a new grad. Five, it gives you a couple more years for the economy to turn around.
2. It's possible, but it's not common. Again, competition for nursing jobs
, especially NICU, is quite fierce right now. Most places will require experience. The new grads who most commonly get jobs in NICU have usually done clinicals or partnerships on those units.
3. No, you don't have to work nights. Although night positions are usually more common than days, there are day positions available. You can also work at a dr's office or clinic that has 8 hour M-F shifts. You have a lot of flexibility as a nurse.