The two quotations are part of the same sentence; not to mention that neither of them are independent clauses. Much like the debate of beginning sentences with conjunctions, most people seem to have conflicting opinions on whether or not the second quotation should also be capitalized.
Leave it uncapitalized. That's an easy one. I think style guides generally concur on that one. And the beginning sentences with conjunctions thing is not really an issue. I would be hard pressed to think of a great writer who didn't do that all the time. Petty pedants care about it because it is easy to remember, but it has nothing to do with good writing. It's just this false "rule" that won't die.
"But of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die." (yes, it's a translation, but it's a great translation.)
"That fence supposedly serves to keep intruders out," Bill states. "Though it only seems to be keeping us in."
It doesn't feel right--or rather, it feels grammatically correct, but not as pleasant to read. In this case, which would be correct?
That one is interesting, because you can do it either way in order to create a different effect. If you want that little pause in Bill's words, you can conceive of the second half as a new statement.
"I rated the story a one on account of it having an end game link on the first page," Bill sniffed. "Though it deserved a zero."
"I rated the story a one on account of it having an end game link on the first page," Bill sniffed, "though it deserved a zero."
Those have rather different rhythms and a different personality.
"I think I've found something in the bookshelf. Perhaps--" Julia tugs at an odd book, pulling it out of the shelf-- "nevermind. False alarm."
There is no rule for em-dash/quotation mark placement. Technically, it can go in or out. In this case, where you have a sentence interrupted after one word, the em-dash inside the quotation marks looks better to me. Notice that actually using an em-dash instead of double hyphens looks *so much better*.
"I think I've found something in the bookshelf. Perhaps—" Julia tugs at an odd book, pulling it out of the shelf, "—never mind. False alarm."