You can absolutely buy on a fixed income with an FHA mortgage providing the buyer qualifies. You could give her the 10% as a gift, perfectly legal. It is all a matter of a lender determining whether her income versus her house payment and debt would qualify for the mortgage amount. It appears from the info you provided, she is a little light on income for a $35000 purchase with 10% down as her annual income equals $8,100 approximately. The first step is to have a reputable lender pre-qualify your mom. Your other alternative if need be and you were agreeable would be for you to co-sign for your mom as a joint borrower.
If you would like the name of some skilled lenders in the Central Florida area, please let me know.
Keller Williams Realty