Plumbing: Does a drain for a bathroom sink have to approach from the back of the sink?

everything you mentioned so far will work the only variable I can't see is the vent. all plumbing fixtures must be vented in order to work properly ( not glug) if when you remove the drywall from the wall there is a "t" fitting you would have to reconnect to the pipe that is going up, as well as the new access in order to have a vent. another solution is to put a clean out somewhere near where it clogs that would make it easy to unscrew a cap and shove a small snake down to unclog your sink without disconnecting everything.

You can drain it any way you like. Why not look into draining it straight down through the floor. and connecting into the main drain below. Many houses drain down under the floor. The faster the drop, the better the drain. As far as the sewer gas smell, you are right, you do smell the sewer. Traps are made to block the sewer smell by using trapped water as the smell barrier, which is why traps are so important. Drains don't usually clog up even when they travel horizontal for long times unless something is put down the drain to block the flow. It sounds as though hair or something else is causing the problem and might need to be addressed. If you still want to reroute the drain you can. the drain is 1 1/2 pvc.

First issues first, Are you on city sewer or do you have a septic device? it may desire to be a septic concern or considerable drain line concern. Are the bathe and bath interior an identical bathing room? If the drains which you have problems with are on the 1st floor and those that paintings high-quality are on the 2d floor it nonetheless may be a considerable line concern, if no longer then lean in direction of a venting concern. they did no longer have %in 1950 so this abode has been reworked. whilst they reworked they could have exceeded over the venting device or no longer put in it correct. they could have put in a mechanicle vent in and it may desire to no longer be working? This vent in the event that they put in one is many times under between the sinks close to the P-capture, it appears that evidently like somewhat mushroom. in case you have one unscrew it to do away with it and notice if this enables the subject, if it does replace it whith a clean one.

And the winner is; The vent Must be reconnected and if you run the pipe the way you want to the vent will be gathering waste. The easy button is to treat your drain once a week and avoid putting grease into it.

The plumber used pressure fittings to make the tight turns. Drains have to plumbed DWV fittings which have a wider radius. They take a up a larger space. That's why the plumber used the pressure 90 to make a tight turns in the walls.

you could switch it but there is no good reason for it to clog much now, unless there are some restrictions or there is not enough drop after it enters the wall or you are putting stuff in it that doesn't belong.

it is unlikely the layout is the problem

I cant see any problem with it you will be eliminating two bends makes sense to me. One bit of advise when you reroute use a sweep(long turn) ell to connect to the down pipe no sharp turns.

No reason I can see why that wouldn't work. But to be sure you will have to open up to see if they had a reason - they sure created more work for themselves. Either there is something strange in your building code or they approached it from behind because, "That's the way we always do it."

the clog may be cost by hair accumulations ,try to add first some chemical to dissolve, you can buy it from any hardware store.

ya I agree with your new design ( the white line ) since it is shorter and going to save one elbow .

That looks fine. Doesn't mater which direction it drains as long as it drains "down".