Okay, I have looked at the rules, and here is my DM's ruling:
1) When possessing your familiar, you can only use your familiar's abilities, not class abilities. As another example, a druid cannot wildshape their familiar into a bear. So you CANNOT summon an echo whilst possessing your familiar. This is irrespective of what you can an cannot see.
2) An echo cannot hide, nor can it be hidden. So it can never qualify for a sneak attack from hiding. If the PC uses their bonus action to switch places with the echo then they are no longer hidden. The PC can set up a sneak attack from the echo by way of being an adjacent ally though.
Those are both really
not good rulings from a RAW/RAI perspective. I mean, obviously, your game, your rules, but the first doesn't even resemble 5E's rules, and the second, whilst not as far from them, does go off a basic misunderstanding (one that has been discussed).
1) - Just straight up
made-up rules with no basis. A Druid couldn't wildshape his
familiar into a bear (obviously!), but he could definitely wildshape
himself into a bear, whilst viewing through his familiar (not sure why you're using this word "possessing" - this isn't what's happening). You don't "become" the familiar. It isn't wildshape or polymorph or something. You merely view/listen through it. You're blind/deaf from your body like you've put on a VR helmet, not "possessing" the familiar. You still have proprioception (particularly important here), touch, smell, taste, heat/vibration/etc. and so on.
The actual rules, for reference:
"While your familiar is within 100 feet of you, you can communicate with it telepathically. Additionally, as an action, you can see through your familiar's eyes and hear what it hears until the start of your next turn, gaining the benefits of any
Special Senses that the familiar has. During this time, you are deaf and blind with regard to your own
Senses."
Note that it is an action to do this, so you can only move and do things that are a bonus action/reaction/free action/no action. So that's what would stop you doing Wildshape, unless you somehow had two actions, not anything else.
2) An Echo isn't a creature, so no it isn't an "adjacent ally" for anyone and you're not going off RAW and it's questionable if it's RAI for the rest, so...