Backdoor entry defends using VS. willpower + firewall. if the host is unaware, willpower will be 0 dice, so will only defend using Firewall.
If the host is 'attended' or 'monitored' (which is different from 'unaware') by a security decker spider (or anyone else currently monitoring the host) then the host will defend with the willpower of the spider plus its own firewall. If it is not attended by a security decker spider then it will defend with its only firewall as a dice pool of its own. There are even an explicit Host Hack example on SR6 p. 178
1) what is a spider?
SR5 p. 216 Matrix Jargon, Cont - Spider
A security hacker/rigger employed by a corporation or law-enforcement agency to protect a physical space or a host from hackers.SR6 p. 173 Matrix access and PANs
They use personnel, known as security spiders, to protect their Matrix investments.2) What are a spider's stats?
A Spider's willpower is whatever you set it to.
5 is a good number.
You have a professional rating 3 (minuteman security) sample rigger on SR6 p. 206 (willpower 4)
You have a professional rating 6 (doc wagon engineer) sample techno on SR6 p. 208 (willpower 5)
You have a professional rating 8 (spec ops level) sample decker on SR6 p. 209 (willpower 5)
3) Can you "fight" a spider, like a persona, once its been engaged in defending its host? Can a spider be defeated, or you must defeat the host instead?
Yes. It is a real person with a matrix persona.
You don't have to defeat the host before engaging with the spider.
You don't have to defeat the spider before engaging with the host.
The host will defend using its own IC no matter if there is a spider in the host or not.
4) Can you perceive a host being controlled via a spider using Matrix perception, or other actions? is there any way to become aware that you are now facing much tougher opposition because you blundered, or the patrol IC alerted someone/something?
From outside the host? No, not really.
5) can you do things like "trace Icon" on a spider to find the control room in the building you are entering so the street sam can put a bullet through the head of the person causing the Decker such problems?
Yes, but you first need Admin access on the network that the spider currently belong to (which would normally be the same as the host).
Spider being part of the Host network would typically defend against your trace icon attempt using his or her own Willpower plus the Sleaze rating of the Host network.
Stainless Steel Devil Rat answered most of your questions, but I got a few nitpicks where I don't fully agree with his answers (because some things seem to have changed from previous edition and this edition):
4) A Spider, like any other Persona, can run silent.
Note that in this edition it seem as if either the entire network is running silent or it isn't (unlike previous edition where individual icons could run silent). Also, once you gain user or admin access to the network you automatically spot all icons within the network. It is impossible to even use the illegal hide action if the observer is already inside your network (and in this edition you cannot 'attack' and 'kill' the access level of the hacker as you could with the Erase Mark action in previous edition).
A spider will most likely be part of the host network.
and Noise doesn't exist inside Hosts
You are thinking about previous edition (where hosts where normally everywhere and being inside a host indeed gave you a direct connection to anything connected to the host which in turn let you ignore noise modifiers). In previous edition it was highly likely that the spider was not physically close to the host.
In this edition being connected to a host does no longer give you a direct connection. It also no longer let you ignore noise.
If you had 4 points of noise to reach the host you will still suffer for 4 points of noise while inside the host. In case the host is linked to a physical location (which is a thing in this edition) it would be highly likely that the spider is also physically close to the same physical location.
Yes. But to be pedantic and clear, a Host is one kind of icon, and IC have another type of icon called Persona.
To be pedantic and clear, in previous edition Host was one Icon and access (marks as they were called) was on a per Icon basis.
In this edition, however, 'Hosts' are made up by a shitload of different icons...
SR7 p. 173 Icons
Icons are a very broad category of Matrix objects. People have icons, called personas. Devices have icons. Hosts have a ton of icons, from the places they sculpt to the individual items that fill those backdrops. The software that you use has icons, and the security protocols chasing after you have icons, too....but it doesn't really matter and you don't really need to keep track on different icon types anymore since access is now instead tied to the whole 'network' rather than individual icons. Doesn't really matter if you have access on a device connected to a host or if you have access to a host. It is the same 'network'. If you already have access to the 'network' then you already have access to everything connected to the 'network'.
Speaking of, there's no reason there couldn't be a BUNCH of spiders on duty, if you wanted a particularly robustly defended host...
(but only the mental attribute of one of them will count as the defender of the host)
And yes, if there is no spider on duty (due to scheduling, or the hacker being victorious in cybercombat) then there's no "defender" per se.
Against for example the Backdoor Entry action the host will defend itself with its own firewall acting as a dice pool of its own and when using for example Data Spike on the Host's Patrol IC it will defend with the data processing + firewall rating of the host even if there is no spider monitoring the host....
There's no way around launching 1 IC per round.
(I know you mean that the host cannot launch IC quicker if a spider is present, but for completion sake and for other readers I just want to mention that the Suppression Complex Form may be used to delay IC from being launched once per round).