It doesn't matter where you get what. You need to be stamped out of Thailand, and in Laos. You can't get back into Thailand if you are stuck between two countries.
You absolutely need to cross the bridge to border bounce/run. To enter Laos, you need your visa on arrival which is on the other side of the bridge. To go there, you need to take the 35 baht bus like everyone else. There is no way around it. Then, when you have the visa, you turn around and leave Laos. Then take the same 35 baht bus back over the bridge. Then, you enter Thailand with visa exempt entry.
Also, those dedicated line I've not seen that for a very long time. And this is part of what I said about not arriving there went group bus are also there.
There is no agent at that border. Only thing they have is some "fixer" that will hold your hand in the process and then drive you to Vientiane. But the numbers of people paying for such useless service is very low (only some first timer). Nobody is losing time over not doing this.
Second, if you take a group bus you won't save any time at the border, unless you don't know the process at the border to begin with. You follow the queue like everyone else, you do not skip line. In fact, the reason why the queue can be long is if you arrive at the same time as a few of these buses that go from Udon to Vientiane. If you are unlucky you arrive at the same time or slightly after and can be a lot of people ahead of you. But if you plan ahead and know went these buses usually arrive, you will be fine.
And on top of that, OP is talking about a border bounce, not visa run. Border bounce mean u cross the border, turn around, and come back immediately to Thailand 10 min later, or few hours if you want to shop around. You do not go to Vientiane went you border bounce.
I've use this border probably 20 times since 2010. The last time around 2 months ago.
1) Most people can get visa at the border, no need electronic visa application in advance.
2) No need car in his situation. He just want to in and out quickly. The bus over the bridge is like $1.
3) Yes, I can answer that agent is never beneficial at that border. Whether it's to activate a Non-O multi entry, visa exempt, etc, no need for an agent.
4) No need to stay the night or to show any proof of. Very easy hassle free border.
In general, I always advice people to not use google as a reference for questions like these. Real life experience is much more reliable.
"How easy is to make it alone without any agent ?"
Very easy
"Is it really prohibited to walk or use your car at the Thai–Lao Friendship Bridge No1 and cross the bridge to Laos ?"
Car need paperwork, not worth it. You can walk if you like hour+ walk, but the Bus is like a dollar to the other side and take 5 min.
Can i simply pass the Laos immigration check point on arrival, then turn around, exit Laos and enter Thailand again? Do they accept it ?
Yes, you can. You get your Laos visa on arrival at the booth there and then turn around the corner 30 meters away and can leave Laos, retake the bus over the bridge, and re-enter Thailand.
(I did not wish to stay or visit any place in Laos at the moment)
Thai citizens can enter Laos only with Thai ID card or passport is required?