If there is a complete sentence in the quote then it makes sense to put the full stop inside the quote marks. There isn't any need to put a second full stop after the quote marks, as it is obvious that a new sentence is starting.
On the other hand if there is no full sentence in the quote, you don't want to put a full stop in the quote, but as the sentence is ending, you ought to have some punctuation, which would go after the quote marks.
If the sentence in the quotes is a question, it should have a question mark (in the quotes) You could put a full stop after the quote in this case, but it probably isn't required.
You asked, "Are they correct?" There is no simple answer to this.
I wrote, "simple". But there may be a longer answer that is possible.
You said, "I know it's grammatically correct." That is true but rules for punctuation are about clarity, style and rhetoric. These particular rules are different in the USA and UK, so you should consult a style manual.
One can construct sentences that are difficult to punctuate well, such as a question with a quoted question at the end. In general avoid extra punctuation after a quote that contains a complete sentence.
Did you ask, "Are they correct?"