It depends really. If they look completely off...then I might not get around to playing it. But if I read about a character and find them super interesting/likable I can ignore the art.
For me it's the artstyle and the seiyuus. Even if the story seems "uninteresting" I'll play it if the first two appeal to me. Sometimes I'm also surprised as the story turns out to be fun despite the synopsis.
I think it's up to you. Personally I restart from the beginning because my memory is terrible...so I might not remember certain details that happened during the routes I did complete.
I'll stick to one otome game as I always play an otome game and another type of game. So I stay with the otome game until I finish it then switch it out for another.
When I was like 6 or 7? I didn't know it was an otome game. Just a game my older sister had. Found it fun that you could choose how the story ends and was addicted ever since.