Trying to install my new oil cooler on my 2.0 4 motor. The bracket that goes on the side of the cooler opposite the studs is not fitting my oil cooler. Is that bracket needed? Does it provide mounting support or can it be left off?

Yes it is needed. Do you have a new Dansk cooler ? I had to file down the flanges on the cooler to make the bracket fit.
Can you show a picture of the problem ?

It will not "slide" on the end of the cooler it must be clamped on

The oil cooler appears to be about 1/8” too wide to fit the bracket when orientated the way it is supposed to go.

Also, can #5 in the diagram be added later or does that go behind the oil cooler on the short stud?

My most recent motor rebuild needed a new oil cooler. Same problem. Oil cooler a little large for the bracket.

Fixed quickly with a Drexel to the aluminum that was in the way.

Yeah that was my next route. Wanted to make sure there wasn’t something I was missing first.

Check out my build thread. I fixed this recently by trimming the edges of the cooler "sides" with a sharp utility knife.