I think there's a lot of crossover nowadays between British and American punctuation standards. For me, the thing is to be consistent.
I've seen a lot of older books published in the UK where there is NEVER a period (full stop) after Mr or Mrs whereas it's pretty much always been the norm in the US. But maybe that's different now? I've not really noticed it in newer books, I admit.
As to quotation marks, the rule in US is ALWAYS put the punctuation (. , ; ?) inside the closing quotes. But, again, in British usage, I've often seen the quotation marks on the inside, depending on the circumstances. Not so much in dialog, but when using quotes for emphasis, or when using quotes to refer to the title of something.
So, when it's dialog, like
She said, "Go to the store." it makes perfect sense to put the period inside because it's actually the ending of the quoted sentence. And, of course, a second period outside the " would be really silly.

But in a sentence like this:
The book was called "My Trip to the Store".I think having the period on the outside makes more sense. The title isn't "My Trip to the Store." but, rather "My Trip to the Store" so the "." is not part of it.
US English teachers I've known would have one do it like this
The book was called "My Trip to the Store."I've never thought this made sense in US usage.