Hi, we usually only say 'I'll handle it' to mean 'I'll take care of it'. We sometimes say 'I'll handle him or her' but not as often. I'll take care of it doesn't really mean to look after/care for something. It means to solve the problem. It can also mean 'I'll kill someone' but that isn't the only meaning and usually only referenced in movies etc. The third question 'I'll deal you later' is usually used to signify that someone is going to punish someone else for what they have done.