I think this may be what you're looking for:
At the top of their profile page, you should have an option to set some "Filters".
On a PC (Google Chrome), I see it like this:
I was able to filter to Year/Month/Day. Interesting!
You cannot delete messages from someone else's inbox. Deleting account will not delete messages from recipient's inbox. But your name or profile link will not be there once account is deleted. It will show 'Facebook user' instead of your name.
No, once you block someone, that person would not able to see any of your activity.
From Facebook Help Center:
When you block someone they will no longer be able to do things such as tag you or see things you post on your timeline.
From a computer you can. Under your profile, hit the ... button then click activity log, then click filter. Scroll down and select received friends request and select the year you are looking for. If you want just the received friends request save the changes and your done, if you want more options, select them and save the changes then your done.