The reliable way to hire a pro

Air Conditioner is running constantly (it was shutting off after running for awhile and turning back on. Starts blowing strong cool air, then gets weaker after several hours. Discovered water dripping in vent by furnace and pooling on the floor.

In the last 24 hours, whenever I turn on a tap in the house the basement drain starts to fill to overflowing. I've tried using an auger/snake, but it doesn't seem to work.

I'm planning to renovate my kitchen soon and I'm not sure about the best order to tackle everything. I'll need to have the walls skimmed or plastered, some electrical work done like adding new outlets, tearing out the old kitchen and flooring. The new kitchen will need to be installed, flooring put in, as well as tiling and painting. What order should I do all this in? Is there a best way to approach it all?