2 metre wingspan autopilot plane batteries/motors

I'm not the expert, but to run flat in 20mins will allow you to draw 7.5amps continuously. Given the the motor is capable of giving over 500gm of thrust at full current I would guess that after the launch phase is over, straight and level flight should be a fraction of that, I'm guessing that 20mins might be very conservative.

I DO fly electric gliders.
First question, Morgan - have you ever flown an r/c model plane of any sort?
Second question - what model were you intending to use?
Third question - Are you familiar with the UK law regarding model flight - staying within line of sight, not above 400 feet above ground level, not overflying people or buildings etc?

2 metres is not very big, but it is the wing AREA that is more important, more area means it can carry more weight more slowly.
Now, that little motor you show is for small quadcopters, not gliders. For a glider, you want a slower-revving one with a larger diameter and pitch folding prop, hich is more efficient..
Now a battery delivers DC vollts, but a brushless motor requires AC volts 3 phase. So you have to put a speed controller between the battery and motor.
The speed controller will not work on it's own, you need a radio-control reciever to tell it to work.That means - in turn - that you need a matching transmitter to work it!
Now  you said you want to use lithium Ion batteries - fair enough, but they have a lower voltage output than a lithium polymer set - and you need a special charger for either of them. You can't use a 12v car battery charger or a science lab 12v supply - or you'd have a bonfire on your hands!

You also claim that the model will weigh around 500gms or1.1 lb - . That will be a very flimsy model that won't survive much of a knock.
Autopilot? Youll be lucky! You can get self stabilizing electronics, but they are not altitude or course holdng things, they just try to keep the wings level. Every little bump in the air as the model flies will alter the direction it is going in, so that means you have to have full r/c and some way of chasing it, to keep it in sight!

I've just weighed a pair of 18650 li-ion batteries, and they weigh 92 grams., without any wiring or anything!
 

RCTestflight is an American business. They have much more relaxed rules on what you can do, and lots and lots of space out in the desert!
As you intend to chase the model from a car. I suspect that you are going to get snarled up in traffic an awful lot. You might also find that the metal of the car roof will screen the radio signals. Do you know what a Faraday Cage is? Or do you have a rag-top 'sports' car you can take the top off, so you can see the model while it is overhead?
Do you have any idea just how fast your model will fly? I have a powered glider that cruises at 80 mph, and can easily top 100 in a shallow dive.Your chase car will have to go twice as fast, to keep up, or you will waste a lot of battery - circling - while you catch up.
Are there any tall trees, tall buildngs, or tunnels on your proposed route?
Try a little experiment - fly a model you know inside out, then at a safe height, turn your back on it for ten seconds. How long did it take you to reacquire visual contact, and was it where you expected it to be?
I haven't used the flysky radio, so I can't comment on that. I use Taranis and Futaba.

600kv motor, you'll be lucky. The kv number tells you how many rpm's the motor will give for each volt of the power supply/ A 600 will be referred to as a thumper - intended for very large scale models - and will swing a circa 20" diameter prop!. All my motor running on 3S are around 1500 kv.
HobbyKing, in China - USED to have a wide range of motors, and you could look them up on a chart, to find the one you want. I put USED because the business recently changed hands and the website isn't sorted out yet.

Look up Durafly Excalibur!

Personally I can't see any model flying as slowly as 20kph.

BMFA or some other third-party insurance is not essential, but it IS strongly advised, in case you poke a hole in the windscreen of Lord Baggypants' Rolls Royce, or scare his prize donkey into dropping dead!
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You say you are going to chase the craft on a bicycle towing a trailer. You'd need an olympic pedaller to maintain at least 40 kph over your distance! with three people, one pedaller who will be watching the road, one flyer on the trailer controlling the model, and one observer, in case the controller loses sight behind a tree, or something.
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The SUA (Small Unmanned Aircraft) document you refer to expired in December 2020, as far as I can see, and hasn't been replaced.