Zero allowances withholds more than if you claim 2 or 3 allowances. State and federal can be different. The fewer allowances, the bigger your refund and the less you have each payday. It is a trade-off. Do you need more money in each paycheck or do you need a bigger refund- your choice. You do need to be sure you pay enough to not have penalties.
Your state refund is based on several things. You probably live in a state that offers credit for kids and yours have aged out. Most end when the kids become 17. There may be other credits like rent or homeowner's, other home related items. For most states, it is simple math - here is the income, here is the tax, what did you have withheld. You seem to have reached that point that if you want a refund, you need to have more tax withheld at work.
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