The "scores" you are referring to are not experience points or battle score, but rather damage numbers which show how much damage you've done to an enemy tank with a given shot.
The colour of damage numbers indicates the type of damage that was done.
Colour Damage Type Target Destroyed? White Standard No Orange Standard Yes Yellow Critical No Red Critical Yes Additionally, green numbers indicate the amount of health points that a teammate received from a healing source (Isida, various healing augments, drones, etc). Blue numbers indicate critical healing.

Shaft's reload time has been increased to 10 seconds in today's update.

First Sergeant for Vulcan Mk2, and Warrant Officer 3 for Dictator Mk3. You can find unlock ranks and more information on the Wiki.

Reduces damage taken from critical hits.

If you are playing in a browser, cached files will be stored wherever the browser's cache is located.
If you are playing via the client on Windows, cached files will be stored in C:\YOUR_USERNAME\AppData\Roaming\TankiOnline\Cache (replace YOUR_USERNAME with your PC username). You can examine them using the ChromeCacheView utility.

Upload a video to a video-sharing site (YouTube, Vimeo) and post it to the Bugs and Glitches Reports thread.

These are Shards. You can redeem 100 shards for a standard container.

Smoky's critical chance is not fixed, and varies with each shot*. The chance that a given shot will deal critical damage depends on three parameters: minimum critical chance, critical chance step, and maximum critical chance. The numbers you listed refer only to the maximum critical chance. I won't go into the details of how critical chance accumulation works, but you can find a decent explanation here: https://en.tankiwiki.com/Critical_Damage#Explanation_of_probability_accumulation
As for what these numbers mean in practice, the average critical hit rates for Stock, Supercumlative Rounds, and Paralyzing Rounds are as follows:
Mk1 Smoky would score a critical hit every 8-9 shots on average, while Mk7+ Smoky would score a critical hit every 4-5 shots on average.
* Technically, critical chance mechanics are the same for all turrets, but some turrets use parameters that effectively give them a fixed critical chance.

That option does not enable proper dynamic lighting.
In one of the livestreams Hazel gave the following priority order for graphical updates to the game: HD skins, baked lighting, then dynamic lighting. So it's unlikely that it will be implemented any time soon.

I consistently notice damage increases while using Adrenaline - for example, with Striker, at low health, medium hulls take only three shots instead of four shots to kill. Are you sure that you have the augment equipped?
Note that the extra damage that Adrenaline grants is only dependent on the base damage of a turret, and is not affected by damage multipliers such as double damage or Booster. Suppose for example your turret did 1000 damage, and on top of that you received a 20% damage boost from Adrenaline, bringing the total damage up to 1000 + 200 = 1200. If you enabled double damage, you would deal 2 * 1000 + 200 = 2200 damage, not 2400 damage as you might expect. Thus you will not receive a significant damage increase when using Adrenaline and Booster together.

In theory it should. A GTX1650 will be able to run games far more demanding than TO at high framerates.
However, you may not get the performance you expect from TO because the game seems to have optimization issues. I have a GTX960M (much weaker than a 1650) and an i5-6300HQ and in empty matches, I get 200-400 FPS on maximum settings, depending on the size of the map. But I've found that TO seems to be bottlenecked by something network-related; in matches with a lot of players system resource usage decreases and FPS drops, sometimes below 60. This is not a hardware but rather a software issue.

November 20 2020, it seems.
 

Vulcan does not rotate automatically while firing. I think you may be referring to the rotation of the barrel, which is just a visual effect with no gameplay impact. Yes, the augment does not increase the rate of fire.
I can’t attest to how viable either combination is, but Reinforced aiming transmission makes it easier to hit moving targets or hit targets while on the move because of the faster turret rotation speed, so I can see how it could be considered a good choice for use with more mobile hulls.

Yes, afterburn damage begins as soon as the target's temperature exceeds zero. During the 1.25 seconds the target would receive 300 HP of damage (since afterburn does 300 damage per second). It will take 4 seconds for the target to completely cool down (since the rate of cooling is 0.1 units per second), so it will take 4x300 = 1200 damage. If the target is frozen by a Freeze, an augment that inflicts the freezing status effect (for example Smoky's Cryo Rounds), or by Dictator's overdrive its temperature will decrease and you may not inflict the full amount of afterburn damage. The point is that a tank will receive 300 damage for every second that its temperature is greater than zero, and that a tank passively cools down at a rate of 0.1 units per second.

There is a Reload parameter on the Wiki, which gives the time between between consecutive shots in milliseconds. You can use it to calculate the rate of fire.
The gyroscope effect was reduced when Vulcan was reworked, I believe.

You just have to keep waiting and refreshing. Once in a while kits purchasable for crystals come up.

Player count at 15 minute intervals: https://en.tankionline.com/s/statistics.txt
Nice visualization: https://tankirating.org/online

Drones will consume batteries as long as you have them equipped, regardless of whether you make use of their active abilities or not.

The Mysterious Red shot effect was exclusive to the Big Freaking Gun bundle sold on March 2nd, 2020.
More info: https://tankionline.com/en/2020/02/big-freaking-gun-bundle/

List of major updates for returning players

There are several different MDK versions, some of which are in English, on the mapmaker's discord server (link expires in one day).