1) I highly recommend not getting any armor. Light armor is debatably useless, and while heavy armor is good, almost everyone runs AP Ammo guaranteed. If there is one upgrade you get, it's AP Ammo on your primary weapon (except perhaps on Sniper Rifles? You would have to ask others about that).
I would highly suggest the M16/MP5 (or the UMP if you want to save a point in competitive mode) OR the AKM/AK74u depending on your class. Those tend to be some of the flat-out better weapons in the game. Most of the better players use the M16 on semi-auto and just pop the trigger way faster than I can, while the other three weapons are in auto or sometimes single shot depending on long range.
Upgrades to get: AP Ammo, foregrip (though not always required, I don't get it on an AK74u for the Insurgent Scout because I want a suppressor), sometimes heavy barrel, suppressor sometimes, possibly 1x optics (red do or holo sight) on the M16/MK18/M4 (if you use these). They fixed awful parallax issues recently with the 2x and larger scopes, so if you're sniping a more legit scope is fine, and sometimes a 2x on an AKM or M16 is a good choice for the map. I almost never go with a secondary weapon (I rarely run out of ammo, can pick up weapons off the ground, and I actually often die from reloading too early versus running out of ammo mid-fight anyhow). An exception here is to definitely get a handgun if you are sniping with a bolt action weapon, or possibly if you are using a semi-auto rifle with a huge zoom scope.
Smokes are SUPER important on some maps (if not most) on Push. Frag grenades are also awesome. I often carry a frag grenade when smokes aren't needed and in many scenarios on firefight. It's just so much better to clear a room that way than risk death because the guy proned in the perfect corner will often outshoot you.
If I have more points, I can go with a chest rig to pickup a smoke and a frag grenade (2 more points for a chest rig and smoke), or if I want two frag grenades I can go chest carrier (2 points, heavier) with a frag grenade in explosive slot 2 (this gets me two frags for only four points). If you want two smokes, you can just do smoke, chest rig, smoke for lower weight (I think?) instead of a chest carrier with smoke in explosive slot 2.
When you have a chest carrier (2 points), explosives in explosive slot 2 come in a quantity of 2 (though you can't put C4 in explosive slot 2, for instance).
If the gametype is skirmish (there is a cache to blow up) I prefer to have a Molotov or Incendiary on me (they are 3 points, are okay as area denial, but it only takes one of these to blow up a cache, whereas it takes two frags to do the same).
Flashbangs so far seem underwhelming to me. Even when perfectly placed, the other person can still blindly fire right where they know you are coming in (and are already likely pointing).
C4 is pretty good. You can put it on a point on the story above or below you, then just blow it up if someone comes onto the point but isn't on the same floor as you.
RPGs/ATs are great if you are that class. It can be a toss-up between that and an under-barrel grenade launcher. You can only ever have one RPG/AT at a time, so a chest carrier doesn't do much for you, and your weight is often close to max, so I'm not even sure if you can do an RPG with two frag grenades in explosive slot 2. A chest carrier might be good with an RPG to just have one grenade or smoke too. RPGs clear out rooms by firing into doorways or windows from relative safety. You can also pick them up off the ground. They destroy caches well too, but I have often suicided doing this.
Speed is important in this game. I often run an M16/MP5 (this gun is great, probably better than it should be just because it's so easy to kill people in this game, and the recoil is really manageable), AKM/AK74u, iron sights with AP Ammo and foregrip and/or suppressor, then a frag grenade (or smoke). That's it. Extra points when available go in a chest rig or carrier with more frag grenades. If I somehow still have points, then perhaps heavy armor. It depends on how fast I need to get to a point on initial spawn.
You can also change points up when you no longer need smokes, or you are well into a round and are respawning (it might be better then to get heavy armor instead of a chest rig/carrier with an extra grenade, since you might not need to rush so fast to get to an area first, and you might be at risk of a spawn camp).
Even if you snipe, play the objective! This could be making an ambitious move when you are last man standing, or it could be paying attention and moving towards an objective when you and the three other people on your team still alive are all trying to snipe/hang back. If nobody is on the point and the enemy is capping it, they will get a full respawn. You will probably lose at this point.
2) For practice, I often just hop into an empty server and run around. You can also join a nearly full server, jump off a team into spectating, and spectate the most successful players (not always those with best KDA, often those with good objective scores too, but even those aren't always 100% best for indicators of good play).
3) Honestly, this is kind of irrelevant. It's a number that means nothing. Currently, the devs are looking into developing a matchmaking ranking system. This would solely be important to prevent severe skill mismatches, as well as give some sense of progression I guess. One of the best parts about this game is that you are not disadvantaged by not having enough rank/experience to unlock the 'cool' or 'best' weapons or attachments.
4) Lick the Butter has a good youtube channel. You can also google or youtube search for "Insurgency Competitive" to find some good gameplay. Competitive videos are based on 5v5 scenarios, which do play out well on many of these maps. If you want to play the competitive mode, type "mm:comp" into the search bar when looking for servers. You can then play that game type (different point values and different availability of equipment--no C4, some classes have heavy armor, some don't, etc.).
5) I'm not that into mods, but feel free to go crazy. Some servers will force you to play vanilla, but you can just hop to a different if you really want to see/hear your cosmetic mods while playing.