It may be one of man problems she is dealing with.
I truly think a total going over by family Doctor is in order in case she has an ear infection( would / could throw Eqilibrium off )
I believe she is scared hence the shaking after the falls .
More recently you said she fell backwards hurting her back.......this could have done some serious damage to her spine or coxic
As for the eating perhaps many small portions thru out the day would help out with this
Really I believe a Doc's visit is most essential right now
Yes I know here in Canada a Home care support Worker would be gotten in thru the doc's referral
I know of many here that have some in 3 to 5 hrs per day that comes im 7 days weekly
Also talk to the doc about this whilst there
I hope you get some help and your Mom
Please post and let us know how things go Okay
Take care and God Bless'
Keeping you n family in my thoughtas and Prayers