Oil in the gearbox refill/testing/engine oil question (10W40,5W30)

Hello, Since some of the gears are a bit rough (especially 2. if it is cold) I would like to check the oil level in the gearbox. Is this possible without further ado? Bzw where can I refill oil, and in this context also the question which oil. Apparently the original should not be undisturbed. The best. I also noticed during the holiday trip that the engine oil was almost empty (purple rod dry) I foolishly forgot to check because the last oil change is not all too long before the Now the gas station keeper (Austria) just filled me in 10W40 instead of 5W30 (1l) he said that would be better because not so fluid blah.. has surprised me so quickly that I could not react at all. Is that actually better? I think Ford doesn’t say 5W30 for fun.