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It means the base loan amount, before the upfront mortgage insurance premium, cannot be any more than $353,750. If you are just looking to put down the minimum 3.5%, that means your sales price would have to be no higher than $372,368... as $353,750 is 96.5% of that figure.
To your second question, it depends on what the builder is defining as "closing costs", you should ask for a breakdown. They will also need to specify a dollar amount or % of the sales price as the credit in order for the loan to be underwritten. The upfront MI can be financed into the loan though, it usually is for FHA.