Replace laminate flooring around back door with.. tile?

Hello all,
I have a lab puppy. She's gone through most of her destructive phases
as a pup, but I'm left with some of her damage. Plus some damage from
an improperly installed door.

Ok, so here's what we got. The previous owner very poorly installed a
pre-hung door in our house. You can see the jamb is all crooked and I'm
sure he didn't seal it properly. The dog, was nice enough to show us
all the wood rot damage we had there by digging it out, and making
quite a mess. At first, we thought it was just the jamb, but it turns
out it (somehow) got under the threshold and into the laminate flooring
at the door. So the laminate flooring had begun to bubble up and crack.
and now I can see various layers into it.. It must be removed.

I personally only like Tile at exterior doors to absorb moisture
(especially here in Texas). So I'd like to make a very small tile entry
way (this is actually a backdoor which is part of our living room, so
asthetic suggestions are welcome) I'm looking to install maybe 6-9 sqft
of tile tops. What I'm not sure how to do is:
1. Remove laminate flooring just around door area. Seems like it must
be cust straight so a threshold between the tile/laminate can be
installed to hide the seam. Don't know what to cut this with. *** It is
installed on a slab.
2. Do something clever with the wooden baseboard that adjoined the
laminateflooring and the wall. Maybe I don't need to do anything here,
maybe new tile will slip nicely underneath?
3. What else?

I'm mostly concerned about how to make a nice even square/rectangular
area for the tile without ripping out all of those boards.

Also, I've never installed tile, Do i need to put something over the
slab, or install it right on the slab. How do I align the heights?

And yes, I know I need to replace the door, that's part of this
project. I can handle that.

Thanks for the help!!
-Brett

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