What a fun ask I'm totally not doing to procastinate on cooking... XD
Arthur Pendragon is, in my head, demiromantic and bisexual... It sort of depends on the circumstances/episode. Arthur needs a very long time to really feel connections with people and only starts to consider love after he really gets to know them, hence his constant search for true love in the show. With Merlin I'm not entirely sure if he was attracted to him instantly, strangely enough feeling a connection from the moment they met, or if it takes him till the end of the series when Merlin confesses his magic and finally shows his true self to realise the depth of his feelings.
Merlin is, well... Bi Bi Bi. A disaster bi in fact. With a preference for sweaty men in metal boxes, he's not very peculiar. However, Merlin is a one person hyperfixation kind of guy. Most people are convinced that Merlin's gay.
Gwen: I feel like most people in BBC Merlin are bi and Gwen is no exception. Like Merlin, she prefers the hero type in metal uniforms. But she also had a thing for Morgana in the beginning.
Morgana: lesbian. I have never seen a woman so disinterested in men, I'm not surprised that they casted Katie McGrath in supergirl as supergirls love interest. I might settle for homoromantic and asexual. But definitly in love with Gwen in the very beginning.
Sir Leon, my beloved, the immortal, the one and only, the eternal suffering aro/ace. I don't have to explain this one. The only counter moment is the Lamia episode where Leon suddenly develops interest in women out of nowhere. My personal take is that anyone could be fallen under a Lamia's spell, this one just had a taste for men (and male presenting).
Sir Elian: once upon a time I clocked them as nonbinary and sadly that's as far as I thought into this character. Pretty sure he's aromantic. He/they pronouns. I dunno, I don't think Elian would conform to anything if given a choice. Aromantic too, I think. Like Leon, there is no interest there, but he does play around with Percival and Gwaine quite often, so I'd take that as allosexual.
I am excluding Gwaine because I think canon Gwaine is written as a straight oblivious fuckboy. Albeit a kind one XD fanon Gwaine is often poly/ pan... Or into apples. Lmao XD and I'm not sure about Percival because the man has a dead wife and kids.
Keith: with his lack of interest in women, he can only be gay. That man looks at no one quite the same as he looks at Lance. what the hell was the whole bonding thing if not a hint for post canon klance? Sorry, not sorry XD rivals to best friends to lovers.
Lance: *bi bo bi* bisexual lighting Lance. Doesn't matter if you prefer klance or shallura, this man is a walking bi flag. I don't know what you mean by proof, just look at this wiggly boy with the fingerguns. He can't even sit straight! Can't do math either. He's perfect!
Shiro: probably the only character in my entire history of shipping that I would unqueer without feeling bad about it. I know he's gay, I just don't really see it in the writing. Of course there aren't always clear signs that someone is gay which is why this is good rep actually (+he's married), but you asked me for proof in the show and all I see is that this man is a dad. That's his gender and his orientation and that's all I really need to know.
Pidge: aro/ace because I love my aroaces and this child loves robots and robots only. Also nonbinary/genderqueer. Pronouns: fuck/off XD
I think Lotor should have been bi. Pre-canon Lotor had us Langsters ship Lotor x Lance and it was so much fun :D
Bob: gender: evil, orientation: villain. I hate this guy
Coran: the georgous man is either gay or pan. More likely pan because I vaguely remember he had a son?
I hope I answered your question reasonably enough XD thank you for the ask, anon :3