The self-installed tiling in the bathroom is visibly crooked, and the joint between the wall and floor is not flush.  

I am an electrician by trade and own a 1916 home myself so the commonly frightening buzzwords such as "knob and tube", "plaster walls", and "asbestos tiles" don't carry quite the same weight with me but it will be nice to have someone who is as objective as possible.If you feel comfortable answering, could you share what you budget for repairs on these older properties?

Tile or linoleum?

I had to prime and paint all walls, put tile in both bathrooms (we created a second one).

Keep in mind that no one has x-ray vision and stuff will always be revealed once walls/cabinets/tile starts coming down. 

Re tile the bathroom showers, paint kitchen /bathroom cabinets, new countertops, and painting of house interior.    

Tile and granite and glass shower doors.

I'm thinking about:1 replacing the counter top from tile to some other cheap alternative2.

I would also suggest finding local supply stores to find out where you can buy tile, kitchen cabinets, bathroom vanitys and sinks.

My contractor handles paint/tile/cabinets/ basic plumbing/ electrical/ lighting/ trash/ fit and finish / cleaning it up when done.