This thread is more than 4 years old......
Having said that; in 5th edition you switch to silent running before you take an Attack action, otherwise you will automatically be spotted.
...and there are some mistakes in the example (I just read it):
Noise is measured at your location. Distance to hosts in the 5th edition is zero.
You don't measure the noise the actual physical library (unless you happen to be hacking the host from there, but in that case you should probably establish a direct connection by using a cable from your cyberdeck to a device slaved to the host or physically touching it if you have skinlink echo in case of the TM, this would also let you ignore host ratings as trick or force your mark upon the host).
Marks are placed on the host, not the other way around. In the text Slicer picks up a library card and Vixen has a mark. Should rather be that he place it on the library host and Vixen placed her mark.
To locate a specific file inside a host you take the Matrix Search action with a base time of 1 minute, not just a matrix perception test as it is resolved in the text.
Running silent give you a negative dice pool modifier of 2 dice. Text does not account for that.
Patrol IC is noticing a persona that is looking for a file. Nothing illegal in that. Looking for a file is a legal Data Processing action. Running silent is also not illegal (but it is a bit suspicious - should probably gone in without running silent, unless perhaps it was after closing hours and the host is expected to be empty).
Nestled hosts was not a 'thing' in the 5th edition.
If you are spotted then you can take the Hide matrix action to become unspotted (this is optional and not really a mistake in the text, however, it would have been good to showcase it)
If you are marked then you can take the Erase Mark action to remove the mark (this is optional and not really a mistake in the text, however, it would have been good to showcase it).
Once things started to get heated Vixen could have just compiled a crack sprite and ordered it to retrieve the file while she exited the host and just waited for the sprite to complete his tasks.
Marks are individual. The Host has its marks. The spider has his. You can't 'share' your marks. Spider need to place his own. Instead of slicer gets a third mark it should be host place its third mark on slicer.
Edit File action to copy is opposed by host ratings. This is normally one of the hardest tests during a pay data run since you can't directly connect to the file in order to ignore host ratings. In the text no test is needed.
Tracing a sprite lead to the physical location of the technomancer that compiled it.
6th turn 1st pass. Vixen could have placed her mark on the file. And then taken the full matrix defense action, in the same initiative pass. Full Matrix Defense does not cost her the complex action, she still get to use it. That way she could have copied the book at initiative pass 2 with initiative score 11.