Two examples that express the difference between the two tenses: - I was looking for my watch, when i saw that i was already late. - i looked for my watch this morning, but could not find it. For the difference between looking for and searching, i'll redirect you to https://www.italki.com/question/79339

There is no difference in meaning between those four phrases.

I was looking for > You spent a period of time in the past to find something ( continuous tense of look) I looked for > You tried to find something in the past (past tense of look) I was looking for my shoes the whole day , but where ever I looked for it , I could not find it. "Look for" is just to find something you want . To search is to find something missing or lost or required by you. I search the Internet for more information . I am going to look for my dog > to find your dog I am going to search for my dog > Can mean you dog is missing, and you are going to find it) The 2 words can be use interchangeably , but search indicates "lost to you" or "missing from you"

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.