I switched from VR to AR way back before HB ever left the car. He's been running in AR since then because, by my understanding, your body is insensate while in VR. Saint and HB have been walking halls so HB couldn't be in VR.
As I mentioned in my IC post, rebooting erases all marks placed by/on HB. So those door and camera marks HB placed to get us all in would be gone and unable to provide security any information in the timeline that you outlined. Unless, of course, you mean those marks HB has placed since reboot (which isn't entirely clear to me) but, see below...
Per the Hack on the Fly action hopping to a grid which one doesn't have access to doesn't mark the host. The host has a defense and if HB beats it he gains access. This action shouldn't alert the grid even if unsuccessful. If unsuccessful then HB wouldn't be able to do anything on that grid at all, as far as I can tell.
Good point with the marks being cleared. The only mark I cleared when you rebooted was the one on the host itself, when ALL marks would have been erased. I'll update the post to reflect that. It doesn't change much, however, as the Spider has found the cameras offline, which would have led him to conclude those areas were likely to be infiltrated.
It does seem like you're getting "grid" confused with "host" though. There hasn't been any mention of a grid yet (unless I used the term incorrectly by accident) because so far we've been treating the Matrix as only existing on a single grid. Grids are like your service provider. Any grid can access the matrix. The rules mention penalties for being on a lower-quality grid, or a different grid from someone else, but so far this has just been ignored for simplicity's sake.
A host, on the other hand, is a specific closed network within the matrix (like the home network created by your router). You can't access a host without permission. You can obtain that permission by marking the host. Most marks are obtained by presenting credentials to the host as a legitimate user, but hackers obtain marks by using hack on the fly or brute force, depending on their style. The CTI host is where all the various CTI devices and IC and network security people are. You can't get to those things without going through the host, and illegally marking the host absolutely does start your overwatch score. Simply entering the host once it's marked is free, and does not increase your overwatch score.
I apologize if I have inadvertently used the term "grid" incorrectly to mean "host" before now. I've been trying really hard not to do so, but I may have slipped up.
To clarify, here is exactly how the previous post rolls worked:
Heartbreak successfully marked the host
Heartbreak entered the CTI host (no roll required)
The Spider found Heartbreak's mark on the host, and erased it (reducing Heartbreak's visibility within the host)
The Spider began to run silently
Heartbreak succeeded in spotting the Spider, alerting him to its presence (but not its location or any other info). He has not yet attempted a Matrix perception test to hunt the Spider down.
Heartbreak succeeded in spotting the icon for the hallway video camera in front of the security office
Heartbreak succeeded in marking the hallway video camera
The Spider noticed the video cameras and door alarms that were offline where the runners had entered the restricted access area (I mistakenly had him notice the marks on these devices as well. That will be edited now - thanks for catching it!)
Heartbreak spotted the icon for the comlink radio device in the security office
Heartbreak marked the comlink, and overheard the radio traffic between the security teams
The team exited through the door on basement level, and are currently in another restricted hallway, and are now on their way to the security office
Heartbreak will be able to monitor the video camera in front of the security office, and the radio traffic between the security teams, as long as he maintains his marks. The Spider has a chance to spot these marks, though.
