If you need the job more than they need you, then you can ask for more money. However, you really should have thought everything through before the second interview. I would clarify the health insurance. I would also clarify whether you are hourly or salaried, because this will make a difference. If you are salaried , you will get paid for your sick time but you will not get paid for overtime. If you are hourly, it could be the opposite.
If you are serious about becoming a programmer, you will need to work very hard and not complain, and hope thy like you enough to give you a chance. That they said 15/hour in a newspaper ad doesn't mean they have to pay you that. It's not like they are going to put "around 15/hour" in thead, even though that's what they may mean.
If you do take the job, it doesn't mean you can't continue to look for other work.