I’m afraid I can’t help with the meaning, but I can with the contractions!
Update: Oh! Actually, I think I do know what it means, now that I looked more into なきゃ! “Unless your relatives collapse, you won’t come home?”
This is the contracted form of 倒れなければ. 倒れなければ > 倒れなきゃ. So this would be an “if… then.” (If your relatives don’t collapse, then…)
This is the contracted form of 帰ってこないのか. The て form will only be a request/command if there’s nothing after it (and even then, it could just be a hanging て form to soften it, rather than a command) because it’s a shortening of てください. Here, 帰る is in the て form to attach the auxiliary verb くる (来る), in this case in the negative こない, which gets contracted into こん. The の (also sometimes ん, but you can’t have two んs in a row, so either it’ll remain uncontracted as here or the second will get dropped) will often go after the plain form before か because using か directly with the plain form can be rather rude. Just の will also be used to form questions with the plain form and is softer than のか or んか and thus is probably used more often by women (though men will definitely use it too)
As you continue reading, you’ll get a feel for the contractions better! Until then, we’re always happy to help. Here, also, is a quick contraction reference that someone else compiled on the forum.