The table itself isn't going to help too much, so I'm here to give more detail on your abilities. Hopefully at some point I can get the SkillSoft working so this can all be beamed into your head, but for now, this'll have to do.
This action will let you change a detail or two on anything you own in the Matrix: your Persona, your Sprites (if you have that much control over them), your own Nodes, you name it. Keep in mind this is changing how you are seen in the Matrix, and not much else. Anyone who's after you won't be looking for your signature Icon, they'll be looking for IP address data, signature details in your code, anything that you can't easily hide with an Icon Swap. However, this doesn't mean this move is purely cosmetic, just mostly. A lot of getting in to where you shouldn't be includes looking the part, so looking like a normal partygoer in a Matrix Club can make for good cover. Just remember that no one's getting fooled if they bother to double check, so be ready for your cover to be blown immediately.
Pretty much what it says on the tin. If you have access to a Matrix connected device, you can freely change its mode. Ganger about to shoot a friend with their AI assisted pistol? Turn on the safety. Want to make a distraction in an office? Set all the printers to copy some meme for all eternity. Need security to back off? Wait for them to enter an elevator, and then force it to go to a different floor! The sky's the limit! ...so long as your access ID's trusted. Also remember that you only get one Free Action per Initiative Pass.
If there's a Node in signal range, you can find it. The main limitation is it has to be Active or Passive. If the Node's offline, you won't find it. Similarly, if the Node's in stealth mode, you'll need to be more proactive in your search.
If you were anything but a technomancer, this would just be a quick way to turn off your Commlink. In VR, it immediately causes dumpshock. The problem doesn't come from dumpshock necessarily - if you're smart about it you should be able to swap to Altered Reality and jack out. The problem is that us Jacking Out severs our connection to the Matrix, which means we lose connection to our Sprites. If this happens, you'll need to reestablish the link to your active Sprites.
Lets you change from AR to VR, and vice versa. Keep in mind that your body will stop moving once in VR, so don't just swap over unless you're sure nothing will happen. [p.145 for rules on initi pass]. And be careful! If your connection is being forced open by a Black IC attack, you won't be able to change mode!
Lets you terminate downloads. Not just your own, but any you have the proper Access ID or subscriptions to stop. For example, if a download is happen from Node A to E, and you have access to Node C, you can force the download to stop. This might not be the most effective on popular Nodes that have a lot of fallback servers to transfer through, but will be very effective when stopping downloads from fairly unknown Nodes.
It's like speaking, but on the Matrix! Additionally, this can be used to activate a device or agent. Like telling your soykaf machine to make some esspresso, or telling a Sprite to hack someone's Commlink.