Missing pullstart screw won't cause the leak, but should be replaced. Sounds like maybe you should retighten all the nuts and bolts. Get yourself some blue locktite and use it on the screws to help hold them tight for a longer period time. Go thru the entire car and remove one screw at a time, put blue locktitre on it, and reinstall snuggly. Be careful not to over tighten and strip out the hole.

Remove the muffler, hold your finger over the exhuast pipe, and blow into the end with the rubber coupler. It should not leak air.