Let's say I have a type rating for an Airbus A320 and applied for lets say delta. So we know that Delta has an Airbus A320, Airbus A330, Boeing 737, Boeing 777, etc. Suppose I have an Airbus A320 type rating and I applied and passed the interview and everything, will they automatically assign me to the Airbus A320 considering I already have an Airbus A320 type rating , or not? (By Airbus A320, I mean the Airbus A320 family which include the A318 A319, A320, A320 neo, A321, A321neo)
No. You'd take the same initial course as everybody else, learning that airline's procedures & checklists for that aircraft. Having a type rating shows the hiring people that you're able to pass the training course & checkride for that level of aircraft, and that's good to have. But beyond making the aircraft systems part of the syllabus easier for you, having the type won't change your training.
It also probably won't affect which aircaft you initially get. Those are based on where the airline needs pilots, and then (typically) on some sort of bid process. The airline presumably expects all its new pilots to be able to complete whichever training course they get, so your type and/or prior experience is unlikely to drive your initial assignment.
For a new, small airline in need of hiring captains off the street, things might well be different.
No, you would begin as an entry level FO with Delta. For that airline it would probably be the MD88 airplane.
If you only have a type rating, in their eyes you only have enough knowledge to be dangerous. They are probably going to want real world PIC/SIC jet time in addition on the order of 500-1000 hours of it, in addition to night an instrument time. I've never heard of the majors demanding a specific type rating to new pilots as they will train them to operate their aircraft the way they want.