There are specific guidelines when you are vacating your own residence which you own to move into a new home & you are aiming to use rent from the vacating residence to qualify. With FHA financing, you will either need to relocate to a new area not within reasonable commuting distance OR you will need to prove you have 25% equity in the vacating residence. Since you own your current condo free & clear, after some minor research, the lender will be able to figure out you have the 25% equity and so you would have the chance to use the it's rental income to qualify for the new home. However you will also need a signed lease agreement covering the 1st year of the new FHA mortgage you are getting (so if it's a 1 year lease effective September 30th, and you are closing on the new home October 5th, it won't cover the 1st year, it'll be 5 days short) and evidence of depositing the security deposit and/or 1st months rent. Conforming financing (Fannie Mae/Freddie Mac) has similar requirements, except they require 30% equity instead of just the 25% like FHA requires and also reserve requirements (aka cash in the bank after you close).
In order to use the equity from your current condo as the down payment on the new home, you will need to get the equity out by doing a cash-out refinance on your condo. Since you won't be planning on living in the condo for the first year of the mortgage, the refinance will need to be done as a non-owner occupied occupancy type. It's a little tougher to qualify for non-owner occupied mortgages on a condominium, but it can still be done. If you purchased the condo with cash because it couldn't be financed by a mortgage lender (due to a high investor concentration in the condo complex, too many people past due on their HOA fees, etc.) then you may also find doing the cash-out refinance to get the equity out to be a bit of a challenge. Taking the cash out will still allow you to have 25% equity in the home (in order to use the rental income), because cash-out refinances on non-owner occupied properties will only go to 75% of the home's value anyway.
FHA mortgages don't require that the borrowers are married, so you and your boyfriend can get an FHA mortgage as long as everything qualifies. I am actually doing an FHA purchase loan right now for a boyfriend & girlfriend, with one of their parents co-signing and providing gift funds for the down payment. FHA is pretty flexible in that aspect.
To really know your options though you will want to get more than just "message board" advice. In my opinion you'll want to talk to a patient loan officer who will walk you through the entire process and covers all of the bases.
Shane Milne | Lending in all 50 states | NMLS #81195