Can you pour a cement wall against the exsisiting inside rock basement wall?

Yes,

I had a client that did that in an old home in Saint Louis. It took a long time but it looked great and made his basement much nicer.

Some really old homes with stone walls do not have a footing at all - if you pour a new footing you have to do it a section at a time and pour it under the old wall as you go.

You could run rebar steel from floor to ceiling to help support the wall, also run steel into the old stone wall to tie it together.Clean the loose fill and pour a slurry of cement into the form.

He started with a 4 x 8 piece of plywood (laid side ways) around the basement and then poured it in from the top, working his way around the house, plugging holes as needed. Good luck

You'd have to transfer the load from the old foundation

to the new support.

Beam hangers aren't designed to support the rim joists, ( the supports for the house frame), they work the other way.

This is a job for 'pro's who have 'on site' knowledge of the structure.

Something can surely be done, but it needs to be done right.

Get estimates before you negotiate a price for the house.

you could have the whole foundation pointed , inside and out for a lot cheaper than what you are talking...if you are going to go through the trouble of pouring footers , tear out the stone and lay a block foundation....

no, if ive got it right, when you build another footing inside the existing you are not supporting the outer wall, just the floor joists. think about it