留学したいものだ - The first part, 留学したい, is being treated like a tangible object. Emotive excuses, exclamations, nostalgia, desire, beliefs, etc.., which have been nurtured by the speaker for sometime are expressed as if they're real.
約束は守るものだ - This is a very strong way of saying what one ought to do, something along the lines of "Promises are meant to be kept" (falls in line with a long-nurtured/held belief)
父は以前はバスで仕事に行ったものだ - The subject marked by WA is given a particular characteristic, 以前はバスで仕事に行った.
生徒はもっと勉強するものだ - Long held belief. Drop the MOTTO, and we'd have a characteristic.
