Mang is definitely not a horse. There's no common reference or understanding that Mang represents a horse. Maybe you heard it wrongly or it's a made-up term in a very specific context that's not widely known.
I've never come across the term 'mang bts'. It could potentially be a nickname or a code word within a particular group or community, but without more context, it's hard to say for sure.
It depends on what you mean by healthy. If you're talking about the ingredients and cooking methods, some of their offerings might be considered healthier than others.
I'm not sure exactly what Mang BT21 is. It could be a fan-made manga based on BT21, or a special edition or spin-off of an existing BT21-related comic.