1 - Go to the room where you get transported to after killing Rom, the Vacuous Spider. There you can be transported by standing near the door leading to the stairs and letting the hole grab you (aka,
if you have enough insight), but only if you have the Tonsil Stone. If you do not, you will simply be grabbed and killed.
To get the stone, you need to kill Amelia and have entered the Forbiden Woods. After that, just talk to any red lantern NPC and they will give it to you. I think you're too late for that tough... If so, you won't be able to go there in your current playthrough,
2 - Go to the back doors of the clinic and explore it for a surprise.
Here's a way to get there:
https://www.youtube.com/watch?v=nlLPVQXqzWA
3 - At the end of the Yharnam's sewers, there will be a tunnel with a big pig inside. Kill it and see the item it drops.
4 - Yes, if you want to fight an opitional boss. If so, consume 3 umbilical chords and look for any opitional boss you might've missed.
5 - Not much, just a farming spot for twin shards and stuff:
https://www.youtube.com/watch?v=_ZPs19s7PlU
6 - I'm not really sure of what tools you're talking about. Can you be more specific?