cars can operate without a fan due to bad fan clutch, just hot. either way, they aren't expensive. change it out.
yeah, new stat, coolant flushes. a couple coolant flushes w/ new coolant. drain before and between. and of course.. make sure you've bled the air out of the coolant sys.
course it could be oil pressure problem. maybe a galley is clogged. but that would require major work to the internals, so you should check everything else first.
you've checked sensors already, which wouldn't really effect the temperature all that much. at least.. you wouldn't be able to drive it or whatever someone else on here will correct me with.
something that can sortof change the temp but not extremely change it without you noticing the obvious, is that the radiator might have too much shit lodged in it. no airflow through the radiator metal folds and it's not going to be cooling the coolant or drawing air to the fan too well.