Okay, than back to the commlink example...
What can the TM do within a targets commlink?
i.e. can the TM switch a hacker who is running in cold sim to hot sim?
From my understanding of hot-sim modified sim modules, either you're moded for hot sim (and running it) or you aren't. It's a hardware, not software, question.
Can he take a picture with the integrated camera and send it to someone?
I would argue yes, if the account he's using to jump-in has the right access permissions (ie, if the commlink is configured to require admin authorization to delete a file and he doesn't have admin, then even acting via jump-in, he couldn't pull it off). Mind, this one is fully GM fiat, other GMs might be more, or less, restrictive.
Can he delete the memory without the hackers knowledge? a.s.o.
You see there are many little things in question.
I think if it requires a program to do it (like the Edit program), then you can't do it via jumping-in, only fundamental to the machine behaviors (for a commlink, utilize sensors, change wireless modes, drop/establish subscriptions).
As I said above, this is thoroughly GM Fiat territory.
The other thing is what can the target do against that? The thing is the device has usually no rigger adaption, so that a hacker or rigger can't get the TM out of the control, or what do you think?
I think manual controls always override digital. So, if the hacker notices a problem with his comm-link, he can reboot it using manual controls, dumping the techno back out. If he has admin and the techno doesn't, he can disconnect the techno and delete the account. All the same tricks that work against a hacker still apply, the techno has to get in past the firewall, avoid detection, and be better than the node's owner at cyber combat if he is detected. If the node he wants access to is slaved to another system, it's that much harder to jump in, since now, it won't accept connections except from the master node, so you can only spoof (unless you establish a hard-wired connection).
Another example was the rigged cyberarm. So she is the cyberarm, what can she do as such?
A cyberarm has no visual sensors but a rigger adaption gives usually a set off sensory as base to work, is that sensory base within the echo? That means can the cyberarm see in some way?
Sensors are a function of the device, not the access, so I don't think you'd be granted "cyberarm sight" via the echo. However, you'd have the sense of touch (can't use a cyber arm without a sense of touch), heuristic sense to tell the arm where it is in relation to the rest of the sammy it's attached to, and arguably some kind of "sense" that interpreted signals from the meat of the street samurai.
She can make the cyberarm go limp, she could make it seize up, she could use the heuristic sense and sense of touch to attempt to strangle the street samurai, or shut it down. Not a whole heck of a lot else to be done there.
Assuming it doesn't if the target has an Smartgun and holding a gun with a gun-camera can a technomancer use the gun-cam to see through?
The TM would need to jump into the smartgun, not the cyberarm, even if the smartgun were mounted in the cyberarm, they're treated as two separate nodes. So, now TM has control of the smartgun, but not the cyberarm.
What does a TM with that echo need to control the cyberarm of a fellow teammate, to use her 3-5 IP instead of his 1-4?
If he's got an account with the cyberarm, once he's jumped in, he could control the cyberarm (within the limitations of the cyberarm's senses mentioned above) on his IPs in lieu of the teammate. But, if the teammate needed to coordinate that arm with the rest of his body, he's up shit creek. I don't see this as a good tactic, if the cyberlimb doesn't have an integrated sensor suite to provide LOS.
Over all, this strategy seems too cumbersome for much use, IMO.
If his cyberware or cyberbody is clustert to one node, does that mean if the TM get in that cluster-node she can control his whole body(-ware)?
If he was dumb enough to cluster his cyberware, then yeah, you could treat it as a single node for jumping-in purposes, and thus get control over the conglomerate of cyberware in his body (complete with all senses clustered). Since all your cyberware is already effectively clustered into your brain, I see no reason why you'd ever find someone in this setup, though.
Of course, all this is my opinion, and how I'd run it at my table. I would use the general philosophy that you can only accomplish tasks which fall within the basic hardware (not software) functionality of the device. Other GMs are completely within their rights to disagree with me, because I don't see where the books ever get into what you could or couldn't do with this kind of access.