Almost everything you've said is interchangeable, the one difference between look and search is, search might include " looking for " something more carefully, intensely, maybe with the act of your hands.
Examples : When you go to the airport, they search your bags.
Now i'll try use both of them within a similar sentence
I looked for him in the cafe, i couldn't find him.
I searched for him in the entire building, i still couldn't find him!
The 2nd sentence clearly illustrates the person was looking for something more intensely.
Now as to your " was looking for, looked for, was searching for, searched for "
Again, mostly interchangeable, but was looking for usually indicate a specific moment, or time, usually a recent moment.
" Where were you? - I was looking for the bathroom "
" i looked for my phone, i couldn't find it :( "
Hope that helps.