'Be my guest'
is a way to accept someone's request to use something you own as in the example of a request to use one's phone.
It could also be an invitation to eat,when guests are gathered in the dining room and the host invites them to start eating "be my guest".
It could be used in various occasions and all are an invitation to use something offered or owned by the host.
"Make yourself at home"
means feel comfortable, feel as if you were at your own place,so you can use whatever facility you want,without any awkwardness or feelings of embarrassment .
It is used when someone is asking for something to use or just to make the guests feel at ease during their stay.