When joining two complete sentences, does a comma come after a coordinating conjunction (for, and nor, but, or, yet, so)? Generally speaking, no. But it may optionally come before one.

Also should the title of short stores be italicized or underlined when the title of a book should be enclosed in quotation marks?  There are various conventions about things like this, and I'm not completely familar with them. Generally speaking, the main considerations are to be clear and consistent in how you do this.

Can a semi-colon be used to correct a run-sentence or comma splice?  Yes. But there needs to be some kind of close connection in meaning between the two parts. And it's not good to use huge numbersof semi-colons.  

Lastly, should an apostrophe be used to form the possessives of personal pronouns? 

Consider eg he - his.

Best wishes, Clive