1) There are a lot of unknowns here. What if the tile is cemented right to the floorboards? What if the hallway is the "original floor" laid on top of the subfloor, while the kitchen is just subfloor + tile? You'll need to take some up and see what you've got.

2) I'd worry more if you thought widths (e.g., walls) would change, rather than floors. The one exception was if you were planning some floor-to-ceiling high cabinets (like pantry cabinets) and couldn't spare any height at all.

3) We can't possibly judge this from the single photo you've given us. At minimum, a floorplan to scale is needed, and probably some chat about goals and budget. But really a kitchen planner/designer is worth the time and money.

The tile is higher than the hardwood (I can just make out a
transition in the photo. Tile normally will have a thickness of 1/2".
If the hardwood extends INTO the kitchen (this was not always the case)
then a layer of plywood would have/should have been laid and the tile
laid over it. That means you should have a 3/4" floor height difference
(or more). It is still possible to have the tile sitting on plywood
and NO hardwood underneath....we've seen that before.

You
could check to see the total floor height difference as a start. You
could remove a floor vent to check to see what is underneath the
tile/plywood combination. It is possible that there is only subfloor
underneath.

Let's pretend there is NOTHING under there but
subfloor. You would want to get as close to the original floor height
as possible no matter what. That means tile/plywood removal. At that
point you will have some flooring decisions to make.

And when it
comes to custom cabinetry, they REALLY appreciate knowing the type of
flooring you will be installing. Some floors go in BEFORE the cabinets
(run wall to wall) and other floors go in AFTER the cabinets.

To
make sure your don't have counter top issues (nothing like installing
counter tops only to realize the dishwasher won't fit....because no one
thought to tell the cab/counter top installers that a 3/4" floating
floor was going UNDERNEATH the dishwasher, but not underneath the
cabinets. Telling them Kitchen Designer's responsibility. If the
homeowner is the KD...then it is STILL the KD's responsibility to keep
EVERYONE up to date on these things.

I've seen it happen where
the dishwasher didn't fit with the flooring. They had a choice: cut
the counter top to fit the dishwasher or remove the floor. They chose
to remove the floor (the dishwasher was "bricked" in). Three years
later the dishwasher failed and the flooring had to be cut to get it
out. Home owner needed a whole new kitchen floor...very sad.

Start
with a kitchen designer (KD) to come in and work with your space. They
will have done many renos and will have a few ideas how to approach
this whole "flooring" thing.Basic measurements can be taken with
current flooring. The counter top HEIGHTS will be affected by the type
of flooring installed. And upper cabinets (and their clearance to the
counter tops) will be affected by the floors you choose. And who tells
the cab guys/counter top guys...comes down to whether or not you hire a
professional to help design this or whether or not you are the
KD...which means you tell the cab/counter top professionals what is
going in and how they need to compensate for your decision.