The reason the echo works with the Sentinel feat is because:

When a creature that you can see within 5 feet of your echo moves at least 5 feet away from it, you can use your reaction to make an opportunity attack against that creature as if you were in the echo's space.

But there is nothing in the Manifest Echo's feature that says that it can use your other features or feats. So it won't work with Shield Master or Protection.

As for the third question, yes: you can create an echo in a space you can see, so you can create it in a space that your echo can see, as well, if you're using its senses. The feature says nothing about what happens when you create the echo while seeing through its senses, though:

As an action, you can see through your echo's eyes and hear through its ears. During this time, you are deafened and blinded. You can sustain this effect for up to 10 minutes, and you can end it at any time (requires no action). While your echo is being used in this way, it can be up to 1,000 feet away from you without being destroyed.

I'd rule that you're allowed to keep using its senses immediately after creating a new one, so you can create an echo within 1,000 feet, but you should talk to your DM about that.