those screws are so tiny they're a real bugger to get in without dropping them, like about 1/4", and I seem to remember them being machine threads rather than sheet metal, although regular sheet metal screws may work if you can find small enough ones .... yes, I think you have the right sequence, it's a bit of a struggle but slow and steady wins, look each piece over before you install it to make sure it's the right way round and you have all the necessary fasteners handy - might help to have four hands too

also, I'd use the vent frame held in place to mark for drilling those mount holes, you want them as perfectly placed as you can get
Bill