Difference between BF4 and BF1 armor
Unlike in BF4, where only AT weapons dealt any damage to tanks, in BF1 most weapons deal some (albeit little) damage. Regular frag grenades, incendiary grenades etc. In fact the recent Fall Patch has increased the damage regular grenades deal to tanks.
Another thing is that unlike in BF4 where rear-armor was a tank's weak spot, in BF1 it's the tracks. Tanks can be easily immobilized if attacked from side.
AT weapons
All classes can equip light AT-grenades, which deal much less damage than heavy AT-grenades, but are lighter, and thus easier to throw farther.
Once you level up your assault, you'll gain access to AT mines, as well as the AT "rocket gun".
Snipers have K-bullets, which are specifically designed to damage armor.
Anti-tank rifles spawn as a battle-pickup (for example there is one at E flag on Sinai Desert Conquest).
Field guns and fortress guns also do high damage to armor and can be operated by any class. Their downside is that they're stationary.
HE mortar can do significant damage to tanks without the need of exposing oneself to direct fire.
AT mines, which can be dropped either by Assault or Artillery Trucks are extremely effective - 3 mines can currently take out any armor in the game.
And of course, tanks are vulnerable to bombs dropped from airplanes. The Attack Plane can be equipped specifically for tank hunting.
From the Battlepack wikia page:
Battlepacks are content packages featured in Battlefield 4 and Battlefield Hardline, as well as the upcoming Battlefield 1 that add a new layer of persistance and element of chance to multiplayer.
This would imply that receiving a battlepack is based on chance rather than skill.
Here's another article that suggests you just get them randomly:
Unlike in the past, Battlefield 1 players can earn battlepacks simply by playing the game.
Here's another that explicitly says it's random:
The chances of you receiving one at the end of a match is random; we've heard some players not getting any for a number of hours, while we got our first at the end of our second match, so it's a case of keeping playing until they start landing in your lap.
Based on this article, it sounds a lot like the case system in CS:GO.
Battlepacks are being simplified to a degree. There's now only a single type--a plain old Battlepack--you'll earn by playing.
Although, a major difference between cases and battlepacks is here:
Weapon skins or bonus items you're not interested in can be broken down into Scrap, a currency you can use to buy more Battlepacks, including Enhanced and Superior versions. These Battlepacks can only be purchased with Scrap and guarantee you'll receive higher-rarity weapon skins. In other words, destroying things you don't want gives you a better chance to unlock weapon skins you'd otherwise be less likely to earn through a standard Battlepack.
Best Answer
According to this thread, where somebody sat down and timed vehicle respawns on an empty server, planes have a default respawn time of 1 minute 30 seconds, and tanks a default respawn time of 2 minutes.
However, these times can admittedly change based on a few factors. For example, the server itself has a vehicle respawn setting, which while set at 100% will conform to the times above, when adjusted may result in faster spawning vehicles.
Game mode can also have a perceived effect on vehicle spawn time. For example, in conquest, when having 2/3 points captured, there will usually be more tanks available to your team (obviously depending on the map), meaning that while it may appear that tanks are spawning faster, in fact there may just be more of them in play.
For what its worth my own timing on servers also anecdotally compare to the times measured above, though I was not intentionally timing it as the person in the above thread.