I wouldn't say "at least". I always thought Arthur has been 20 when the series started. He was coming of age in 1x09, which - I think - meant he turned 21. And Merlin must've been about a year younger than Arthur, so, being 19 in the beginning he was indeed still a teenager.
Coming of age was from twelve to 25 in the middle age, depending on the decade, the various stations within the young people's life (own children, marriage, death of parents) and depending on the status quo. I don't know how precise the producers are, though.
Aside from that, I would even believe that Arthur and Merlin were older than twenty or nineteen in season one, given that the dragon's capture had been 20 years already. In case it all started after Arthur's birth, the dragons must have been wiped out within less than just one year, which I think is very unlikely. It would make more sense if Arthur was a few years beyond his twenties when considering that killing all dragons and capturing one of them would take a while. Kilgharrah was the last dragon, wasn't he? Maybe the war on magic had started earlier than people think. Could be that Arthur was 23 or 25 in season one already.
Mordred has always been one of my least favorite characters. Whatever age he will be in the upcoming season, he won't be a nice person but probably just another villain in Morgana's company.