To answer the OP:
Normally if you log out your Living Persona and create a persona on a device (such as a commlink, RCC or cyberdeck) you don't bring any of your resonance based abilities with you.
With this echo you can still Call, Dismiss and Control your already registered sprites (but not summon or register any new sprites) and you can still Decompile sprites and Kill Complex Forms (but not threading any of your own).
Depending on your reading this let you use your existing registered machine sprites to run diagnostics on the device you used to log into the matrix (basically acting as assistants in a team work test to potentially increasing your limits and giving you a positive dice pool modifier).
But none of this is can't already be done without the echo (without the caveat of using tasks), saves you a single task per sprite (with the exception of Diagnostics, which can simply have been set before 'jacking' in with the cybedeck). Unless I am totally not understanding how loaned task works.
Simply command sprite to follow orders of cyberdeck persona. Machine Sprite was set to Diagnostics as it's task beforehand, so you don't need to use another task from it, as it's previously ongoing from whenever you started it. The only thing the echo seems to add is the ability to call one of your sprites, but that could be argued that since you loaned it to another persona, it can call them too (not seeing why you neccessarily couldn't).
If the Spider is physically in the facility, and you disconnect them with Noise, I think they would just wake up in pain and alert security that something just forcibly booted them off the system. If they were a total noob who didn't think a sudden huge burst of static wasn't hostile and was somehow a thing that just "happened", they'd at least alert someone since they wouldn't be able to re-connect. Remember, they're apparently physically there. They'd step out their office or wherever and start shouting at someone. Dumpshock doesn't do enough damage to knock someone unconscious unless they're already damaged.
Correct, but you just completely nullified them for the rest of the combat turn, and the next. That's a lot of free time to do your thing, plus hide again and restart the 'find the hacker' perception checks, usually granting another few IP's. Now hopefully, the spider is smart and comes back better prepared and loads some noise reduction stuff, in reality his DR 3-4 deck, plus datajack, signal scrubber - I don't see vectored filter on any of the spiders in Data Trails, so assume most don't have it. Don't see any with antenna either. So 6-7 noise is the max they could handle. Rinse, repeat the teamwork, edge Jamming test. And another 2 combat turns of freedom from spider. IC is still there if in a host, but in a matrix fight between 2 deckers, it would come down to who goes first most of the time each round to simply knock each other offline again.
To further confound this discussion, what about the the ambient noise? Most areas are going to be 2-4 (that's just using the everyday urban to commercial area, not adding in any 'special' factors) looking at the chart in CRB. How does a commlink below DR 5 ever work even half the time? Why would anyone buy a rating commlink 1-3 if it never worked because noise is omnipresent. Why would a corp sell it? Even the professional rating 4 team has rating 4 DR commlinks... Marcus_Gideon had a really good example about this on one of the reddit forums, but I can't seem to locate it again right now (my reddit-fu search skills suck as I don't use reddit
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With the above mentioned rules weirdness, I would interpet that they lose the wireless listed bonus, but basic connectivity is still there and that the 'funtionality loss' is represented by the penalty (penalize someone enough the action can't succeed, representing blocked by noise), and therefor the decker would just suffer the penalty, not the loss of actual connection. Maybe directly using an actual jammer on the decker as a special case, vs simply just noise from anything... Hopefully that wasn't to jumbled, what I am thinking in my head, doesn't translate well when I type it...
