You read the replies of Loyce in my thread and must've agreed with something he said as you merited the post.
Is it ethical no matter the situation for the manager to join in a contest they are hosting? Even if given permission, should they have even thought about joining?
Back when I was running giveaways for Rollin (around 2016), I was often encouraged to join myself. I'm not sure if I did sometimes, but I do remember I said I don't like conflicts of interests. I tried to find evidence of it but couldn't confirm it. Either way, if you're not in the jury and can't influence the outcome, I'd say it's one of those "not great, not terrible" situations.
Is it ethical to message another managers clients trying to steal them with cheaper rates?
It depends

I think competition isn't necessarily a bad thing. Counter question: is it ethical to charge your client too much and discourage competitors from trying to offer their services at a lower rate? I wouldn't want to be the cheapest anyway, I'd want to offer the best services. Competing on rates is just a race to the bottom. There's always someone in a low-income country that can do anything online for less money.
Rules shouldn't really be changed once contest starts!!
I like having this disclaimer in contests:
Rules
8. We reserve the right to change this giveaway at any moment, and to exclude people from the giveaway if we feel we need to do so.
It's hard to predict all possible scenarios, so if something unexpected happens, it might be necessary to change things. By adding this disclaimer as part of the rules, everyone knows it before joining.
This should of course not lead to for instance cancelling every contest right before it ends, after people spend effort (and money) to join.I have not tagged you myself because it does look like you were allowed to join the contest and there was no rule against it, as well as you were not choosing the winner.