i will answer your questions in order:
1.They say mewtwo went somwhere unknown? he most likely went to cerulean cave.
2.those sentences you listed are probably part of a scientists journal, going day by day, watching the process of creating mewtwo
3. thats probably some coincedince, but you never know...
4. they were probably saying stuff about, well, the player!if any human sets foot here again... it be a kind hearted person... with that hope...you get it? and I dont know who wrote it.
5.what do you mean?! mr. fuji's a nice person who lives in lavender town. if you mean DR. FUJI, thats another story... dr. fuji was the one who came up with the cloning idea and was hired by giovanni, and ran a team of scientists. after mewtwo was created, he blew up the lab and killed every one, including fuji
6.yes. after all, whos the one who hired dr. fuji to do the cloning idea? GIOVANNI! and whos the head of team rocket? GIOVANNI! I rest my case.
7. I dont know what role the mansion plays. maybe the journal was there for safekeeping, maybe the owner found it in kanto. anything's possible
and how these events connect? one way or another, they all mention mew and/or mewtwo