1x4 around the windows is pretty typical-but often 5/4 is used for trim as its finished thickness is more like 1 1/8". The finished size of 1x is 3/4", which can get a bit 'thin' looking depending on the size of what you are casing.

For the opening between the two rooms, consider its size-
If it is a door opening without a door, I'd treat it like any other cased opening.
If it is on a wall with other cased door openings and is the same height then I'd case it with the same size trim.
If it is a wider/taller opening, I'd consider upping the width of the casing, as it is a 'special' item- but I'd do the same method of casing as the others.

Trim parts can be seen as the letters making a word in a language-it has to make sense.

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