My MINI hatch has the 51247132829 spiral shaped bump stops.
I see some other bump stops that are made differently with the number 51247141879.
Can you replace the old spiral ones with these new ones?
If so how would they mount?

 

No.
Sprial ones could be twisted to adjust the height....

 

On the parts diagrams it looks like the non spiral need 2 other pieces, $30 in total, to do the same thing as one spiral stop.

Here's the spiral at ECS for about $9, but shipping seems to be as much as the stop.

https://www.ecstuning.com/Mini-2005-...Hatch/ES92122/

Maybe one of the guys on the forum parting out a car will throw one in an envelope for a couple of dollars.

 

Get the OEM one from ECS Tuning.

Believe it or not, the MINI one is designed not to make noise as the hatch moves/deflects under normal driving conditions when in closed position.

Anything else, the squeaking will probably drive you nuts.

 

There are two different bump stops: the threaded kind (your top pic) screws into the hatch itself. The other blunt-nose kind are screwed down into the lower hatch opening, at each corner, with screws that hold the bumper cover in place. I think that's what your second bump stop pic is.

 

The reason I'm asking is because I'm getting water in my battery compartment and some said that this part can be one possible cause.
So I was wondering if I can convert it to the newer type and if it would help.

 

Not sure, but the third brake light and hatch release handle/trim are other causes of water in the battery compartment. Also check the rear sunroof drains if you have one. The tubes often come loose and leak into the car.

 

If the rubber seal is not doing its job, the car would be kinda loud, and you might smell exaust...and likely hear a clunk on most bumps....
My bet...look at the 3rd brake light, but also there is a foam strip around rear tail lights (seems like my 2005 had it, but saw a few cars that did not have it)...usually if it not there, it not an issue unless water is getting sprayed in there, or perhaps the car is sitting at a weird angle on a hill when it rains? The rear handle is unlikely to be the leak source....it would leak into the hatch, then out the drains on the bottom of it...