I don't think you have any reason for your panic here.
Before I answer your questions, I'll explain the timeline of syphilis.
The first stage is called the primary stage. You'll see a round, open, painless sore at the point of infection anywhere from 10-90 days after infection. The average time for this is 3 weeks. This sore, called a chancre, lasts for 3-5 weeks.
The secondary stage is when you'll see the rash. The rash appears 2 to 8 weeks after the chancre does, sometimes before the chancre heals. The rash is usually widespread over the body, including your torso, palms of your hands and soles of your feet. It heals within 2 months.
The latent stage is when symptoms are gone, but the infection is still progressing through your body, and you won't have any symptoms. This can be as brief as a year, or much longer.
Tertiary comes after, but you wouldn't be there yet if you did have it, which I doubt.
First, your symptoms don't match. A small rash on clavicle isn't a syphilis rash. Oral sex can transmit it, but it's less risky than intercourse.
To answer your questions:
1) As far as I have learnt from different articles and websites, syphilitic rashes are usually symmetrical and widespread on the body, is it correct?
Yes.
2) I've learnt that syphilitic rashes usually appear 2-3 months after sexual activities. So my rashes appeared either too late or too early according to my activities in March and June?
Correct.
3) I had carefullly asked the escort and masseurs about their STD status before visiting them and they all said negative. So, if they did have a chancre in their mouths, could it be easily missed by them?
Chancres are tricky. They are painless, so they can be missed on the genitals if someone isn't checking. However, in the mouth - where you are often running your tongue over things, using a toothbrush, etc. - you are probably less likely to miss it.
4) is it easy to transmit syphilis through the receipt of oral job?
Yes, but syphilis is overall less common than gonorrhea or chlamydia, so the chances of getting it overall are much lower.
Is London still in lockdown? You can very easily put this to rest by getting tested. It's a very easy blood test. I suspect it will be negative.
Can't tell you what that rash is, doesn't sound at all like an STD and if it didn't itch or hurt or anything at all maybe wasn't even a rash. Can't really help you there. If you're that concerned, get tested for any STD that can be passed orally. But I do want to say, asking someone if they have an STD as your guide to whether they are safe to have sex with or not in that regard is a complete waste of your energy. People lie, especially if the only way they get paid is to have sex with you. Sometimes they just don't know, because they could have become infected after being tested if they're having sex with lots of different people. If you have sex with those who engage in a lot of risky activity, you do increase the chances of getting something.
I am also medhelp use like you. I don't know much about std but you don't have to worry about syphilis. Get tested after one or two month to stop your worries.
By the way, I am an overly cautious guy, so I checked my pubic area everyday, and I didn't see anything like a chancre on my penis or anywhere else after the three sexual activities.