Sorry Lepton, some of what you write is just wrong.
Sticking with the Klingons, the correct tactic to hit a target with drones is not to travel at the same speed. Travel faster - ahead of them an average of 3-4 distance units. Anytime the AI sees (4) or more incoming drones (missiles) if it has a wild weasel (massive burst of electronic warfare to distract seeking weapons like drones - shortlived ~15 seconds) it will use them. The advantage to travelling ahead is you can tractor the target with your Tractor Beams. Tractored targets can not use wild weasels (the premise is you have a beam over the target - a launched shuttle, which is all a wild weasel is, an unmanned electronics platform, would not be able to leave the tractor field)
Also, the correct speed is not 10-12. It's actually slower or faster. Some pilots, particularly in "crunch" races like the Feds and Hydrans like to "Starcastle" by travelling very slowly (less than speed 4), reinforce the facing shields, overload weapons and otherwise use a lot of power for things other than movement. This can be beaten, but it's a very different battle than normal if done right. Most of the time, pilots travel much faster, generally averaging speed 22-25 or more. This is maintained by careful power management. Yes using the priorities is useful, but really it's an intermediate tactic to use effectively as it can limit your options if not done correctly. I would recommend using your power slider bars (phaser capacitor at the top of the screen). It's a control slider telling your ship to do maximum recharge of the capacitors (all the way to the right which is the default) or none, all the way to the left. Experienced pilots adjust this first. After the game starts and my phasers are charged, I will nearly always move it to an approximate 2/3rds position for general use. After that, should I have a dire need to go as fast as possible, depending on the circumstances I may move it down to 1/3rd. In rare cases, where I do not want a power drain from other systems like electronic warfare, I have set it to zero temporarily.
A note, improper use (usually forgetting current setting) of the phaser capacitor recharging slider bar can get you killed when otherwise you might survive. Setting it at 1/3rd and forgetting it's there when you're tractored to an opponent at range 2 exchanging shots...chasing an opponent at high speed thinking that any drones the target may launch at you will be killed by point defense which you have carefully turned on...but, unfortunately, you haven't been charging your phasers can be deadly.
About the AI in early battles. In my experience, the smaller ships are hard to fly. They are certainly more challenging and can be more fun, but some of them are deathtraps. That and the AI commonly has a numerical superiority. Systematically and properly used, drones will kill AI easily. The AI simply doesn't defend against them well. When not using large drone waves (like scatter-packs...look 'em up) you have to hit the enemy at your best chances/damage while giving it poor shots.
This mainly means use ECM AND pay attention to ranges when you fire. This means if you're using a phaser 1, get within range 5 - a phaser 2 needs to be within range 3, and a phaser 3 or g needs to be within range 2. Barring an electronic warefare based shift, at those ranges you should be in the 'guaranteed' damage zone. At longer ranges, the to-hit charts are setup that there is a chance that any given weapon will do zero damage in a given shot.
Weapon groups. Pay attention to these. You set them by left-clicking on weapon hardpoints (holding shift key down while doing this to highlight multiple weapons...then when ALL are selected holding the control key down and hitting #1/#2/#3/#4 on the keyboard. Use the ones above the keyboard, not the ones on the numberpad to set them. From then on, if you hit the appropriate number key,you will autoselect all those weapons. I set mine in patterns. Mine is (almost universal on all ships of all races)
#4 - Drones - group them all together. note: I also click on each rack separately and put them on single fire mode rather than fire all at once for a group of 2-4 racks. This allows me selective fire mode for many advanced tactics.
#3 - Primary phasers - Usually only Phaser 1 & 2's. Used primarily when wanting to just fire phasers. Frequently will not include phaser 3's in this on cruisers and larger.
#2 - Heavy Weapons. Disruptors/Photons/Hellbores. Note: On a ship with multiple heavy weapon types, I tend to put ranged weapons here. For the Hydrans, that means Hellbores, for the ISC that tends to be PPD.
#1 - The Alpha Strike. Nearly all weapons although some are removed. Frequently on plasma ships I will not include them here.
ESG's - tend to put them on #4 (as the ship does not have drones)
Fusions - usually #4
On ISC, tend to put heavy plasma onto #4
On ships with multiple types of plasma, tend to put the largest (R/S torps) onto #4
Also, you can always hit the little icon in the ship schematic display that looks like an arror pointing in all directions (bottom left hand panel) which selects all weapons.
More on Klingons. Klingon ships tend to universally have excellent weapon arcs. Looking at the wing phasers (if you look at the ship display, look at the rear secondary hull. The front right and left corners, NOT on the engine pods themselves, are consider the wings. Most weapons only fire in the direction the are on the hull. If you're on the nose, you mostly fire foward. If you're on the right hand side, you fire right only. The klingon wing mounts fire across the hull. The right front wing mount fires ahead and to the right - and then also in a limited arc about 60 degrees directly to the left.
Klingon Boom Phasers (on the nose) are even more interesting. In OP their phaser arcs were properly implemented. If you look carefully at the arc icon, you will see that they fire FX (a 240 degree arc centered directly forward and 120 degrees to either side) - AND they can fire nearly directly backwards. This skips about 50 degrees of arc to the rear sides.
For both the Boom and Wing phasers, this is explained as portions of the ship are physically in the way. In this case, it's the engines. Look at the weapon positions and what arcs are missing, paying particular attention to the position of the warp engines.
What this is really getting at is, Klingons have some wild arcs and they usually can fire all or nearly all of their weapons on an oblique - an angle about 60 degrees to port or starboard of their heading. (ahead right, ahead left) Get within the sweet spot of range 2-3 with them and alpha-strike and see what happens. Do tr to wait until after your opponent has fired at a much longer range. I love turning into an opponent after they volley at range 8-15.
About "weapons not charging". Most likely this is the common display/refresh bug where a weapon icon is not changing on the display to show charge status. Nearly always, it is actually charging. If you left click a single hardpoint mount, look on the weapon panel that pops up just above. There are 4 (race specific/unique) bars that show the charging status of each individual weapon on that hardpoint. If they are charging, you should see them move over a few seconds. If they are not, look at the online/offline buttons. If online, look at your power. Are you going too fast to power them? When you notice one charging but one or more not...AND they're not damaged, it's usually a power shortage. Experiment with slowing down or reducing your power needs by doing things like lowering your phaser capacitor slider bar temporarily or turning off tractors.
Speed flown can be a deciding factor in battles. Not flying quickly enough to outrun a huge volley of drones that you can't stop is deadly. As a general plan, in a high speed battle with a human, if you have the power to fight and go 2-5 faster than your opponent, do it. Do not hesitate to slow down and re-allocate power to charge faster though if the tactical situation warrants it. Can't tell you how many times I've done the above (gone faster) and when I was at a good distance, I'd slow down and reallocate power to prepare for something - then speed back up (reallocating first). But, not all races are designed to fly at the same speed or even at high speed. Some do better at range - some require different tactics to fight depending on what you are flying.
If you really want to learn to fight, go start one on GSA (gamespy arcade) as you can usually get a game 24 hours a day.
All that said, I'm not the best pilot in the world. I am competent in nearly everything. Doesn't mean I'd win, particularly against the many better pilots but I can usually depend on not embarrasing myself too much. Don't mind losing, just mind doing something stupid and not making the other guy earn it.
Nax