Sending a kissing emoji to one's wife in the state of ihraam

Q: On 8 Zul Hijjah in the state of ihram, while chatting with my wife, I sent my wife a kissing emoji with good night message in a mobile, as I usually send to my wife when we chat. I sent it to her just in a normal chatting way, not by lust, she was also in the state of ihram, but she was in next tent to me.

My question is, is there is damm of a badana? Or my hajj is complete or invalid?

Forgetting to remove one's leather socks (khuffain) before 24 hours

Q: I use khuffain regularly in winter and I usually always remove it before 24 hours are up before using them again.

Recently I forgot exactly when my wudhu broke after I put the khuffain on. Since I made wudhu and put the socks on after Asr, it was perhaps after I read my Asr Salaah that my wudhu may have broken. I made masah on them thereafter till the next day. The next day I forgot to take out the khuffain, I made wudhu with masah on them to read Maghrib. My wudhu broke after this so I again made wudhu with masah on the khuff preparing to read Esha. I realised my error, but it was too late for me to make full wudhu to read Maghrib again. So I simply washed my feet, put the khuff on again and read Maghrib again just as Esha time set in.

1. Will my Maghrib Salaah be valid or do I have to repeat it?

2. I read Quraan in this time with that wudhu. Would I have been sinful? Should I read those surahs again (Yaseen, Sajdah)?

Moving to a non-Muslim country to study

Q: I live in a Muslim country. Can I move to Italy which is a non-Muslim country to acquire an mbbs degree and practice medicine? It is neccessary to state that this mbbs degree and practicing medicine is also possible in my Muslim country. I just want to move there due to the extra facilities. So is it permissible to move to Italy knowing that haraam is freely available there?