I am running a plastic 50mm pipe from my balcony through metal fascia and to downpipe 450mm away via 50mm plastic pipe just under my gutter as the channel drain in my balcony did not allow me to have enough fall if I had run this pipe directly into gutter as it would have had to go uphill.
Is what I'm doing OK plumbing wise.

Not sure if I understand your question - but - maintain slope of at least 1/4" per foot all the way to the downspout... Also, you can drain only rain water to the downspout - not sink / toilet / tub or shower. That would have to go to dedicated sewer pipe that empties to the City sewer - not at the curb.

Hope that helps... Back to you... Milo

You are only running 18"(450 mm) so slope doesn't have to be too much, 1/2"-(13 mm.)rain water only right?

Going through the metal fascia (assume aluminum) no problem.
Caulk around pipe to prevent rain water from getting behind the fascia.