The Rules of Shadowrun 4th Ed
Guidelines for determining typical opposition are provided in the Grunts section detailing Professionalism Ratings starting on p281 of SR4Anniversary Edition. Sample groups, their tactics and gear, as well as their reactions under fire are provided. The default assumuption appears to be that these groups exist, the characters are able to inform themselves of what threats exist, and therefore can choose to engage or not, or at least how to engage.
What I mean by this is rather than the GM deciding that the group should run into a group of gangers, the GM and the players are aware of where in the city groups of gangers normally hang out. If the players cross those zones, they know what they are risking, and can be prepared accordingly. Likewise, if they choose to go up against corporate guards, or they know that a corp might hire a hit squad if they get wind of runners sniffing around, they have a sense of what that means.
Run Playtests, Track the results with the players
I don't think you can find clear-cut threat ratings for opposition in the game. While you can generate your own guidelines by carefully tracking what your PCs are capable of getting their hands on, and track the statistics of what numbers of similarly equipped opponents they can handle easily, with difficulty, or only with great sacrifices, you might need to consider another approach.
If you prefer to use a rubric to determine threat ratings, and given the wide variety of options open in the game, experimenting to inform both yourself and the players about the effects these different options can contribute, their average performance with the stats and gear they have, and the limitations of equipment, spell, and skill combinations is a good use of time so that each person has an effective in-universe perspective on what a typical combat will be like.
If nothing else, this will let you become accustomed to setting appropriate die pools for planned and unplanned encounters which won't produce any unwanted outcomes, such as butchering the players by accidentally outclassing them. Once this is done, even if your calculations of a threat are a little off, the players will have enough combat experience to make better tactical decisions - including breaking off the engagement if they notice that the fecal matter is being randomly deployed by an oscillation device.
Allow the players to make informed choices
Information is the real weapon for any successful group of runners. Approach the design of the play environment as you would any other sandbox setting and stat things out according to what makes sense. How many guards does Renraku put in patrol units in their holdings? What gear would they assign? What conventional and runner threats do they normally face and how does this reflect their numbers and loadout? The same holds true for the gangers. What kind of gear can their resources realistically access in the setting you are building? How do they support themselves? How many individuals can those resources support? How famous is this gang, and what are they known for?
Provide information about regions in the city to the characters who are from there. Remind them of it as they cross into those territories so that they know to be as prepared for threats as their characters would be just by virtue of having lived there. Give them the information that they need to choose a threat or choose to walk away, to obtain the specialized gear they might need to neutralize a threat, or to opt for extreme stealth.
In short, set potential encounters, determine the amount of intel that can exist about the threats surrounding those encounters. Make the common knowledge and common sense about the encounter truly common in the player group. Let the group choose to act or not.
Surprise encounters can still happen
Outside of runs and planned encounters, the determination of opposition can still be handled without using published threat ratings, or needing to go beyond those provided in the core book.
If events in the session dictate that something should happen, such as an out of the frying-pan and into the fire kind of event, you can run a seat-of-the-pants encounter by focusing on the characters in it. Build the location for this surprise encounter to allow for interesting and effective tactical choices, including retreat. Remember the pain and shock of injury and possible death can totally demoralize untrained or unprepared groups and make surrender, retreat, or crazed scattering seem like a good idea.
Have a reason for any encounter to take place, and make sure that both you and the players can evaluate the importance of completing their run versus staying in an unexpected firefight 'til the bitter end. Why are the gangers in that territory? Where are they going and why? From where? Who sent them? If they are on their own turf and the PCs intrude, why don't the PCs know about them? What violent and non-violent options are open to both sides?
This is not so much about threat rating as it is about internal consistency in the setting, and the ability of characters to operate realistically within it.
The Matrix
The Matrix can be thought of as the internet. They are very close analogues, and there is generally no case where they are different, aside from how they are viewed.
The differences between the Matrix and the internet are more low-level, existing with concepts such as ownership, and daisy chaining connections. For example, if you connect to a node, and attempt to connect from that node to another node, your access id is sent, which may let you be traced, unlike the real internet in which it would appear to come from another servers ip address.
Nodes
Nodes can be thought of as the publicly accessible webpage of a server, a device would be the server itself. See page 224 for the exact definition, but the point is that every online device creates a node in the Matrix.
Accessing Nodes
Page 224 under "Subscriptions" clearly lists how talking to a node works. If you are within mutual Signal range, connected directly, or by being routed through the matrix you may access a node. Unwired has rules on Noise that effect the last option, but without those rules there is no downside to routing. This means you can access any node from anywhere, with the Noise rules providing some penalties based on distance. You may access a node from anywhere, with some Data Transport restrictions. Most commonly everything is hooked up either wirelessly or using Fiberoptic Lines - in this case, you can assume no interference. Unwired specifically states:
In both radio signals and fiberoptic cables, electromagnetic waves are
used to transport data at extremely high speeds. A data request can
easily make a trip to the other side of the world and back within 0.2
seconds.
However, some nodes occasionally require a different connection: Satellite Links with Geosynchronous orbit halve the Response of a hacker (minimum 1). Beam Links require direct line of sight, and are affected by rain, fog, and clouds if they use a laser. Microwaves can also be used with no environmental considerations.
AR / VR
This is no difference between what you can do with AR / VR. However, VR has bonuses / penalties: In cold sim, you use your Matrix initiative, and receive an extra initiative pass. However, you also take a -6 penalty to any physical action.
With Hot Sim, then you have two extra initiative passes, and get +1 to your matrix initiative. You also get +2 to all matrix tests. However, the -6 to physical tasks is still there.
Generally, if you need to interact with the physical world, use AR. If you can avoid that, then use VR.
Best Answer
The paragraph's phrasing is a bit nebulous. When it refers to extra actions, it actually is referring to characters who are granted extra Intiative Passes by gear, magic, etc. Characters with rating 1 Synaptic Booster will have +1 IP, for a total of 2 IPs - two sets of actions within a single Combat Turn.
Imagine that a troll named Solifuge gets into a scrap with the street sam Gonzales and his mundane lawyer pal, Bob. Solifuge rolls an Initiative of 16 and he has 2 IPs - quick on his feet. Gonzales is sporting some wired reflexes and has a total of 3 IPs, but he only nets 15 on the Initiative test. Bob is hopelessly out of league of these two, going last with Initiative 9 and only 1 IP.
This Combat Turn would play out in the following manner:
Pass 1: Solifuge (16), Gonzales (15), Bob (9).
Pass 2: Solifuge (16), Gonzales (15).
Pass 3: Gonzales (15).
Gonzales has more overall passes available to him in the Combat Turn, but he won't be taking them all consecutively. He also has to worry about Solifuge getting in the first blows in this example.