No, you can not send moshlings to other members on Moshi Monsters.
Yes, if you are a member!
Yes, you must be a member to take your moshling for a walk on Moshi Monsters.
It is not possible to access the Moshling Zoo without being a paid Moshi Member.
This only works if you are a paid Moshi Monsters member. Go to the volcano, do a Super Moshi Mission and at the end of the mission you will receive a moshling. It will be sent to your Moshling Zoo.
You can not become a moshling on Moshi Monsters. You can attract moshlings to your Moshling Garden and collect them in your Moshling Zoo (if you are a paid Moshi Member).
You have to be a paid Moshi Member to have access to the Moshling Zoo through the Moshling Zoo Door on Moshi Monsters.
You have to be either a free Basic Member or a paid Moshi Member of Moshi Monsters to get the moshling Dipsy.
You have to be a member to have your moshling follow you.
No, you do not have to be a (paid) member on Moshi Monsters to get Peppy the Stunt penguin.
Without being a Moshi Member it's not possible to get this Moshling as it's caught during Super Moshi Mission 2.
If you are a member on Moshi Monsters, the latest moshling you have captured will be following you. I'm not sure why though!
There is no moshling on Moshi Monsters named Big Ben.