Commas and periods when quoting

Hello,

I have found the information that in American English a quotation is followed by a full stop which should always be placed inside the quotation marks, for example:

“Diane," she said, "put the book down and go outside for a little while."

To get to the next page, just press the little button marked "Enter."

Is it also the case for the British? Can't we put the full stop after the quotation?

“Diane," she said, "put the book down and go outside for a little while".

To get to the next page, just press the little button marked "Enter".

I have also found the information that when we split our quotation into 2 parts, we put the comma inside the quotation marks when it should be logically there, for example:

"Mary," she said, "I want to tell you something" (in the original sentence there is the comma after 'Mary')

“My bicycle”, she assured him, “awaits me.” (no comma after 'bicycle' in the original sentence)

But there are also people who claim that the comma should always be placed in the first part of the quotation and inside the quotation marks, regardless of the fact if the comma should be originally there or not:

“My bicycle,” she assured him, “awaits me.”

I am quite confused.

Please help.

Thank you in advance.

Shadok