My input on your questions:
1) Since you're actually asking about this stuff, I actually wouldn't mind carrying you if I was on PC (I'm on PS3) since it shows a willingness to learn. I've had level 1 characters be very helpful with power detonations on characters that can't detonate them personally (such as the Geth Trooper's Flamer) but that is rare.
HOWEVER! It seems that Gold is completely saturated with shameless leechers who want nothing less than to actually contribute, so I would HIGHLY encourage sticking to Silver for a bit! I'd say, level all classes to maybe 7+ in Bronze before upgrading. This will give you some extra skill points for power.
If you actually build up a bit of stuff and a bit of experience before going up to gold, the existing higher tier players will be VERY thankful. I've actually added a LOT of less experienced gold players to my friends list to invite me along when they need a hand, JUST because they put in that effort and wanted to actually play the game and not spend all their time dead, seeking out the nearest Banshee just to get killed, leeching for easy credits.
2) Many people will tell you to spam Veteran packs until your uncommons are maxed. It's definitely a cost efficient way of maxing them out, but I'm personally not sure maxing them out is even important, since most of what you ultimately use will likely end up being Rares/Ultra Rares, anyways. The big advantage of it is you'll get low level equipment, like ammo, in higher tier packs instead of uncommons if you max all the uncommons first. Which is definitely a great perk. I'm just not sure it's worth spending all that time deprived of rares, is all.
3) Out of the starting kits, the Vanguard is easily the best power spammer. Since Nova has NO cooldown other than your barriers, and Biotic charge REFILLS your barriers, you can basically do an eternal Charge-Nova-Charge-Nova-Charge-Nova loop. This crap can wreck gold with extreme ease. Afterwards, I'd give it to the Sentinel for their ability to set off easy Biotic Explosions, and durability. Next is the Adept, for having some of the strongest Biotic Explosions in the game (Shockwave is +65% BE damage with the right upgrade, and Warp is +50% with the right upgrade. This class is one of only two that gets both.) It also has singularity to quickly deal with groups of unshielded/unarmored enemies (just throw a shockwave at it!) Engineer is next, It's great and very power based but it doesn't get hefty BE bonuses like the Adept.
The infiltrator and the soldier are easily the most weapon based, with skills that raise weapon damage by a percentage (Tactical Cloak and Adrenaline Rush) and "lesser" offensive skills. The human infiltrator's Cryo Blast is a supportive option that durther increases the damage you can do to armored targets/ immobilizing unshielded/unarmored ones, and Concussive shot, while a fine power, kind of competes with Adrenaline Rush for the cooldowns.
In other words, since you already mentioned using the Vanguard, my advice is to take it into Silver, Spec it so it has 0 Shockwave and 6 in everything else (Many will disagree, but until you get better, you WILL want that bonus to health and shields!) And just charge-nova-charge everything you can. Use the M8 avenger (it's very light for what it delivers) and no secondary gun, for times you don't feel comfortable getting close yet (like Banshees/ Cerberus Phantoms) or for times charging is not an option (Cloaked Geth Hunters/ Cloaked Cerberus Phantoms/ Enemies in areas you cannot charge to.) Use this to build up your arsenal a bit, and then start experimenting elsewhere once you have better guns.