I've seen a lot of people mentioning saving at least what you think the mortgage payment will be each month, but this isn't possible for me given my rent rate. Can that be used as an example of ability to pay instead of the saving?
yes, the mortgage companies (per Fannie / Freddie guidelines) will look to your rent, utilities, etc as demonstration of 'willingness to pay' - be sure those bills are in your name (and not the roommate's name)
however, they will still separately assess your 'ability to pay' (how high is the proposed mortgage payment compared to your income and well as how much 'skin in the game' (the down payment) you have. FHA programs require 3% down. Note that the interest rate (when including the mortgage insurance premium or MIP) is higher whenever you put less than 20% down.