In a manual car at traffic lights when stopped can I put it in neutral but not put the handbrake on but use the foot brake only?

I believe you're in the UK. In that case the US answers are wrong.

The requirement is, especially on driving tests, that if you have time to do so you apply the handbrake and shift into neutral. Once experienced you may find it practicable to just hold the car on the footbrake momentarily, but that's up to you and the circumstances.

Personally, even with the handbrake applied I keep my foot on the brake until I'm certain the car behind has realised I'm stopped.

Yes, you can safely do that, and it is the right way. Keeping the clutch pedal down at a red light may even wear the clutch springs. Never use the parking brake, except for parking. ( well, also it can assist taking off on the steepest hills).

It is not illegal to be in neutral when the car is stopped, at least in my state in the USA.

I agree that it is safer to use the parking brake for taking off on a hill, especially before you are skilled with the clutch. But, I never heard of requiring it on a driving test. But then, my test was a long time ago, things may have changed. Look this up in the official manual in your area. In my state, the manual does not mention shifting into neutral at a red light, nor applying the parking brake at a red light.

In the UK, you can to a certain extent.

There is no law that demands the use of the handbrake, but there is a provision that you don't use your lights in a way that could dazzle or cause discomfort to other drivers (Highway Code rule 114). This could include keeping your brake lights illuminated for a long time in stationary traffic by keeping your foot on the brake pedal, and applies to all vehicles no matter what transmission is fitted.

In a road test, examiners will want you to be in gear at all times. This include stopped at a stop light. So you'll have your left foot depressed on the clutch and the right foot on the brakes while on first gear the whole time. In the real world, this can be very tiring. So I just slip it in to neutral at those stop lights and keep my foot on the brake.

Parking brake is for parking your car only. You always want the brake light on to show other drivers behind that you are stopped.

Most, if not all owner's manuals say to to exactly that:

"When stopped for more than a few seconds shift the transmission into neutral and let off the clutch. Use the brakes to keep the car stopped."

That way you save your clutch, throw out bearing, and engine thrust bearing.

I've heard all sorts of stories that here and there this and that is the "right" or "legal" way of doing things. But as far as I'm concerned I only believe what I've seen in writing and what you've described is what I've seen.

Countries with a separate/higher class of driver's license for a manual transmission are stressing the usage of the hand brake while stopped on an upward incline, for safety, so you don't roll backward while trying to engage the clutch and start moving forward, but, do they expect the use of the hand brake at EVERY stop (level ground)?

In USA, there is no separate/higher class of driver's license for a manual transmission. Many people here could use some instruction in safe driving.

You can but it's not considered good practice since to move off you will have to take your foot off the brake pedal to operate the accelerator. On an incline you may roll into or back into another car. You would fail your driving test if you failed to apply the handbrake when in neutral. mccoyblues hasn't a clue.

With a manual since you need the parking brake to move off from the lights just out it on while waiting.

UK manual test is a fail not using the parking brake.

i use my parking brake when i stop at lights and in neutral. i especially use the parking brake when in an incline. i would put it in first step on the gas until the car wants to move and then slowly let the brake down while lowering the brake at the same time

Plenty of people do it that way. But it's technically illegal. The vehicle should either be in gear or have the handbrake applied.