You have written many things that are correct and false at the same time, but mostly due to lack of knowledge in control apparatus of the central nervous system and human muscles and bone physique and physics. I will try to be basic as possible and give you the necessary amount of information so that you will perhaps understand this more thoroughly.
After learning a bit about HEMA, it seems that technique is more important than brute strength when fighting.
Yes and no. Brute strength is mostly associated with the ability to lift heavy weights, but that is not necessary so. Strength is the result of intra and intermuscular coordination and muscle diameter (which is related to the muscle type and amount of fibres).
Strength power lifter lift relative slowly heavy weights, while the fighter accelerates his fists or feet to a certain fast speed to deliver a momentum ( p = m * v ) to the opponent. Both events result in an Work (W = F * s ( Unit Nm ) ) with a Force (F = kg * m / s^-2).
The amount of Work may be even the same, but the Force is different in both cases.
The muscles are classified into fast twitch (typ 1 and 2) and slow twich muslces fibres. But the same kind of muscles fibres are the main contributer for this kind of Work, becasue the slow twich are only responsible for sustaining a certain low amount of Work for a long periode of time. In other words both the fast 100 meter runner and the heavy power lifter require a high percentile amount of fast twitch muscles fibers, while the long distance runner needs more the slow twitch fibres. The muscle diameter is also different on all athlets. The fighter needs a diameter that allows him to punch as fast as possible, but if the diameter is too high or too low then the punch becomes slower. One the other hand the fighter can pull more weight in kg per cm^2 of muscle than a power lifter.
The intra and intermuscular coordination is a result of the central nervous system neural adaptation to to the kind of exercise. The neurons of a power lifter need to shoot impulses more often to the the muscle fibers than that of the fighters who needs upon one impuls activate more fibers for a contraction.
The power lifter needs different muscles in an lfit attempt at different stages of the movement, while the fighter needs all the muscles involed in the movement nearly at the same time ( very good extreme example is Bruce Lee and his one inch punch ).
I hope that you can now understand what strength is and how it comes about.
Now technique is not so well defined and more difficult to explain so i will be more sloopy. One movement or form of attack requires also and is a technique and several movements combined is also a technique.
The first one needs to be exercises correctly and fast if an window of opportunity is perceived or the defence is necessary. Several movements combined into to a technique have either a goal to open a window of opportunity for a strike and to strike, or to deliver several strikes after each other.
Now i will quote the awsome statement from Conor McGregor: "Precision beats power and timing beats Speed. These are the fundamentals." Think carefuly about this!
Reaction times is faster than action times, and the cowboy who draws second is mostly faster. But what technique you will use to attack and to defend yourself and how well you execute the technique is based on trainings experience and the central nervous system. Precision and timing is also learned through training like Speed (equates to power). Overall in a duell a good training with a certain amount of strengths is better than only high strength with few or no training. And that is the reason why martial arts are trained and why a boxer will beat a power lifter in a fight.
In DnD 3.5 (DnD 5th has fucked it up) terms this would mean that a 10 Lv fighter with STR 14 is better than a 01 Lv fighter with STR 18.
Strength has its place, but generally only insofar as it a much stronger fighter can mask errors in technique when defending against a weaker opponent; you can force an attack away from you even with poor structure if you are physically dominant. However, if you throw too much power behind a cut it's a good way of getting out of line and allowing your opponent to attack into a different quarter. Also, if you do somehow get pas their guard when you over hit you're likely to get your sword stuck in them.
No. There are to many beginner errors here and therefore i will skip this.
Footwork is massively important in fighting, especially when attacking. Coordination between movements and strikes is vital, and knowing the difference between the different times in fighting is of tremendous value. This all seems to be more related to dexterity than to strength.
Now this on the other hand is very correct, besides the last statement. See my answer above.
Also, two handed weapons such as longswords or Dane axes need less strength and conditioning to use effectively than sabres or rapiers do, but one handed weapons generally have a better effective reach.
1 YES and 2 NO! The threat range of a spear can be up to 5 meters, while the sword is up to 3 meters.
Also, off topic slightly but shields are weapons. Especially in viking times when they tended to be the primary weapon to open attacking options when fighting a single opponent, while the sword was there to exploit the gaps that were created by clever use of the shield.
Shields have also the ability to mask your body signaling (in Poker it is called tells).
TL;DR I'd say that if anything STR should modify AC and DEX should modify to hit and damage.
The idea is not stupid, but DEX is reserved for the hand eye coodination and skills like balance, slight of hand and etc. And in an DnD fight this represents the ability to pull body parts from the line of attack, therefore you dont get this bonus if you are constrained.