Lose the battlemap entirely . Use a whiteboard & be more generalized with things like distances & size once the grid is gone. If you're fighting in a huge warehouse district with streets around most buildings. You don't need to illustrate every single building/street.
Don't try for tactical, go for things like "pretty far down the street a car makes a sudden screeching turn pulls down one one of the side streets". The non-exact nature allows the mental theater you mentioned to color in some of the details as the combat evolves. If something happens like a building getting blown up to make some difficult terrain, you have difficult terrain anyplace that seems reasonable instead of "these three squares". Let one of your players manage the whiteboard so you can be free to focus on describing things.
With the grid out the window, a whiteboard in its place, & a player manning the dry erase markers/eraser, the mental theater can spring to life & with the exact dimensions lost to general terms the players stop thinking of movement like chess in favor of describing what they want to do to really add some fire to that theater. If I'm facing off against a rocket launcher with a range of X feet while in my tshirt with a stick, I'm not going to stand at X+1 feet & neither should your players going fuzzy with distance will make it so they stop trying and go with things that play out better in the mind for what they mean from the player's perspective than what they can see from their external godlike view of the situation as a player.
How can I include a shaman as a bad guy for a run that the players need to deal with. Where can I read about Shamanism and their role in the setting?
My Shadowrun experience is mostly 1st and 2nd edition but I don't think the fundamental idea of a shaman is that different in any edition of SR.
In Shadowrun a shaman is, traditionally, defined by their totem. The totem heavily influences the personality and drives of most shaman. Some would say the totem shapes the shaman and others contend that the shaman is drawn to the totem that fits their "true self" best. There are countless origin stories of shaman that support one camp or the other. The end result is the same, shaman and totem spirit are of like mind. So pick the totem accordingly.
If you want to use a shaman as a foe pick a totem that fits. It doesn't have to be that this NPC is "evil", it could just be their goals are mutually exclusive with the goals of the party. This can even work out to be more dramatic as, from a certain point of view, the goals of the NPC can be understood. So, for an urban shaman I'll go with a Dog, Raccoon, Rat or Raven. All of them will do well in a city and make excellent foes but not necessarily evil foes. Dog is very loyal and a true defender, imagine being on the wrong side of a Dog shaman. They don't give up and will not stop coming for you. Raven would be fun too. The motives of a Raven shaman could be very mysterious. In some cases they have none, it was all just done for the fun of the game or as misdirection as Raven strikes in another direction. And if you really want evil it is hard to beat the Spider totem, such a shaman is a mastermind, plans within plans having counter plans with backup plans. Also, if there is an SR4 variant of the toxic shaman that will really cause the PC's trouble. The toxic spirits of the cities are twisted creations full of all the foulness better living through chemistry can create. They are brutal and brimming with rage.
As to how the Shaman fits in with the world, think about it like this. The clash between old and new, magic and tech, the rational and the spiritual are heavy influences in the world of Shadowrun. That was kind of the point with having a world in which magic and tech stand side by side. While Shadowrun looks like a high tech, future world setting it is much more. It is a world that embodies the duality of the human experience. The comfort of what is old and has always been next to the trill of new creation. That is magic and tech. Friction.
That said it should be noted that not all Shaman are Luddites. Shaman will use tech, some more than others. That seems to be influenced by the person's life before hearing the call of their totem. And some totems have less problem with it in general. Take Raven for instance, the spirit is a classic trickster and may well find some forms of tech to be fascinating and rife with possibilities for entertainment (tricks). Fox may use tech at a critical moment just because the opponent would not expect it. On the other hand a shaman of Eagle will be one of the least likely to ever use tech of any type.
While Shadowrun:Denver is mostly 3rd edition it is the most expansive Shadowrun repository I have found. It has a section for fiction that has some stuff you may want to read. The log section may be entertaining as well. There is a section for...everything. Go and check it out, you may spend days reading.
If you have the time to read some of the Shadowrun novels do so. They can do wonders when it comes to helping you get a feel for the world.
Best Answer
Basic rolls
You roll as many d6s as your Attribute + Skill for the intended action. Each dice rolling a 5 or 6 is a "hit". If there is a difficulty, the "net hits" are the amount on hits above that difficulty.
"Basic" combat mechanic
1 - The attacker rolls the appropriate attack skill + attribute + modifiers.
2 - The defender then rolls the appropriate defense skill + attribute + modifiers.
3 - You then compare their results. If the defender rolls more hits than the attacker, or on a tie, the attack misses. If the attacker rolls more hits, the attack succeeds and the net hits is added to the weapon's Damage Value.
4 - If the attack succeeds, the defenser then rolls Body + Armor - Weapon Penetration. Each hit reduces Damage Value + net hits of the attack by 1.
5 - Finally, you apply the final Damage Value to the defenser as wounds (i.e. nothing if it is reduced to 0).
This is the combat mechanic reduced to its "simplest". However, keep in mind that a LOT of modifiers and exception then apply, depending on whether the attacker or defender is moving (or both!), whether anyone is behind cover, the weapons rate of fire, who is already wounded, recoil, and so on.
Drones and Magic
Drones and Magic are both two extremely complex and detailed systems of the game, therefore it is almost impossible to sum them up in a couple of sentences. I will give some guidelines, but take them with a truckload of salt.
Drones have their own mechanic, but basically and in a lot of cases, there will be a hacker using his Mental attributes + hacking skills to attack/defend instead of standard attribute/skills.
As for Magic, there are even more things to take into account. In a lot of situations, spells will be cast using a Mental Attribute and the Spellcasting skill, and will be resisted either through Willpower or normal defending attributes. They also cause damage to the casters. Remember though that there are a LOT of different spells, of ways to cast them, as well as Adepts and Spirits.