An Echo cannot surprise creatures. An Echo cannot make a hide check or roll initiative.
As an aside, you seem agitated Mistwell, or perhaps I am misreading the subtext. Regardless, I hope all is well.
The Echo Avatar power allows the Echo to be up to 1000 feet away. Nothing states one cannot still use the features described at 3rd level. If your consciousness is in the extended range Echo Avatar....logically why wouldn’t one be able to roll initiative. The essential
you that is your consciousness is there in the Echo Avatar.
Technically your consciousness is more present in the Echo, then when viewing out of a Familiar.
While the Familiar responds to your commands, the caster of Find Familiar is just a remote viewer with a telepathic comm link. The Familiar is independent, though compliant.
By RAW your hidden Rogue getting the benefits of being hidden on attacks through the Echo, should work.
I’ve detailed my objection to the implications of RAW, and explained what my table ruling was previously. You seemed fine with it then.
While I like the Echo Knight as a subclass, there still seem to be quite a few rough edges and grey zones regarding how the subclass features interact with the system.
Theoretically a Druid/Echo Knight could summon an Echo while in Wildshape, (and potentially boost their Con modifier for Echo Knight powers).
Echo Avatar is a good scouting vessel, if the vessel is destroyed and you have Reclaim Potential at 15th lvl, you just got an 2d6 +Con Temp HPs.