生活を送る is a common expression. 送る has several meanings, and in this case it means to spend your daily existence.
For 「また迷ったりすることがあるのもしかたがあります」
The expression is not moshikata,
It's ga aru no MO shikata ga arimasen.
First of all, the "mo" means something like "also" but with an emphasis.
And shikata ga arimasen (not arimasu) means it cannot be helped.
"<noun>がある
の" can be translated "<noun>がある
こと". Basically, the の turns 「時々寂しくなったり、また迷ったりすることがある」 into an adjective.
So the last part of the sentence would mean something like there'll be also situations where I felt lost but it can't be helped.
である is a more formal way of saying です.
BTW, for the 口がうまい/いい話をします thing, when I used "smooth talker" it was for the lack of a better word that I could think of. I guess smooth talker has usually more negative connotations (though not always) since we typically associate it with salesmen etc. Perhaps "glib" would be a better word since it's more neutral? Even for 口がうまい there could be negative connotations depending on the context.
5)私のように日本で留学生活を送っている人が大勢います。自分の国は色々違うところがるので、時々寂しくなったり、また迷ったりすることがあるのもしかたがあります
okutteiru?? Isn't okuru give? What does the moshikata here means?。
6)カラオケは日本人によって考え出された遊び道具である。
Why use de here? (de aru)