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Give it more time. Once you start getting much better cards, then you can start thinking about closing it.
depends on utilization of your credit line for the most part. I'd leave it until your file grows a bit.
I plan on doing the same with Walmart and Amazon the minute I get something similar to both. Sallie Mae has 5% on Amazon, and 5% on Groceries. That would kill two birds with one stone. Care Credit I think is a keeper because it's WAY more useful than I thought it would be. Despite it's overall lack of benefits, the 0% on medical expenses is a big help.