I rent in a 1930's house.

I was wondering if the outlets ( a mix of 2 prong and 3 prongs all over the house) were grounded through the use of the BX grounding the outlet-boxes themselves.

Tested the 3 prong outlets with an outlet-tester, got 2 different results on 2 separate outlets: one giving me open ground (no ground existing) and the second being hot and neutral reversed. I think I can conclude outlets are not grounded.

That s why I was wondering if the boxes of the outlets were grounded through the use of BX,
And if they are then I would ground the outlets to the boxes by adding a ground wire.

Also, did they use BX back then, or different cables?

I have a fuse box, where the neutral is fused also.

Thanks

The keyword here is "Rent". Which means you cannot add anything.

The LAHJ usually will allow homeowners to pull permits but renters cannot. Either the Landlord or a licensed electrician acting on behalf of the Landlord can pull a permit.