YAY! So glad you are actually doing matrix things and not hand waving it to an NPC. It's also neat to see a character who isn't a dedicated decker, they've got other things they're doing too.
1: Using a cyberdeck, commlink and Image Link (cyber eyes) I guess he can access the Matrix in AR or Cold-sim VR? Since Hot-sim requires a Cyberjack?
No, he can go hot sim. pg. 267 "All
cyberdecks include hot-sim modules". He has a hot sim module (cyberdeck) and a direct neural interface (datajack), those are the two things you need to do hot sim VR.
2: When do we start rolling Initiative? First when encountering the IC Pat at Host B?
Nah, only if combat starts. The Patrol IC can't automatically see the decker, because the decker has a Sleaze attribute. If the Patrol IC spots the decker (its job is to search, after all), THEN initiative can start, cause the decker probably wants to do something about that.
3: When he enters the Matrix (he is physically parked around 20 meters for the computer in the garage) do he need to do a Matrix Perception or will the garages Icon be right next to him?
This part is up to you. The GM has to paint the matrix world as well as the physical one. Would the garage have a public facing icon for people to interact with, or is it secret? People don't need to make perception tests for things that aren't hidden.
4: When Host A is probed/brute'ed is it correct to use Action: Control Device, to open the garage doors?
Yes, but it's not the only option. Deckers can get away with a lot using the action "Spoof Command" - which you can do with Outsider access (ie. you don't have to be in the host). Think of Control Device as the action you use to sustain use of a device, and Spoof Command as the action you use to do one-shot actions like "open door", "unlock maglock". To take over the security turret in the ceiling, I need to Control Device. But if I just want to command it to shoot the guard over there, I can Spoof Command.
5: Can the IC Patrol be "killed" before it get's to activate the SCRAMBLER (if I got a lower initiative) using Data Spike?
I'm not really up on the intricacies of cybercombat. But probably yes.
6: Is IC Patrol really only doing a new Matrix perception test every 20th Combat Round (1 min)? Seems like the player will have enough time to get done with the job?
Treat it like a real guard. Sensitive areas will be scanned more often. Alerted guards will scan more often. Large systems that operate inefficiently (government databases) will be scanned less often. Treat 1 minute as a guideline, not something to announce to your players. However, if the decker does good legwork, maybe they find out the patrol interval. If they're having an easy time of it, maybe give them another scan right before they get the thing they're after. Yknow, for dramatic purposes.
7: Would the smartest approach be to use Hide Action before probe/backdoor entry on Host A?
No, it's not necessary. Hide would only be useful after the Patrol IC has spotted the character. That's when he becomes no longer hidden. It has no effect on your OS. As long as the decker is running silent (pg 178), they are considered hidden and can only be spotted by a successful matrix perception test.
8 Is it correct that a "Security Spider" is another Decker in the matrix? CRB mentiones Spiders but no rules or specifications can be found in CRB.
Yep, it's a decker that's protecting the system. Read the Host Hacking examples in the book (pg 178, pg 188) to get a little more of an idea of what they do. Emphasis on little. Spiders 'live' in the host - the host is the spider's web. Low security hosts may have no spider, or perhaps the company has hired matrix security from another company and there's one spider checking on 10-20 hosts simultaneously, so doesn't appear very often. Even if the spider isn't currently present, you should use their stats when the host's rolls call for it. It represents the defenses that the spider has set up. Spiders can leave the hosts they defend, IC cannot.
9: Noise: I guess Noise is only a problem in AR since in VR you can just "move" to the Icon and start hacking?
No, it's a problem in VR too. No matter where you "move" in VR, you're still tethered to your device's physical location. Personally, I'm not a fan of the Noise mechanic. It's there to discourage doing a shadowrun from your bedroom, to keep the decker with the rest of the team, so instead of counting negative modifiers on a chart, I just tell my players they need to be within a couple hundred meters.
10: Host B (Got the file with the adress): Would the actions be: Crack File -> Edit File, to copy the adress? After the Hack and Enter Host actions.
Here's the possibilities:
It might start with Matrix Perception or Hash Check to find the file, if the player doesn't know where it is/it's not obvious/it's hidden/there's a lot of files to search.
Next might be another Matrix Perception to inspect the file, to get some info on it. They might learn if it's encrypted, if there's a data bomb, when it was last edited, etc.
Next might be Disarm Data Bomb
Next might be Crack File to remove encryption.
Finally would be Edit File to copy it.