What is the best and safest way to fix my protruding mouth and sloping forehead? (Photos)

Sounds like you have a lot of concerns about the shape of your face. First remember KISS, keep it simple sweet heart. There are many procedures that can be performed  on your face so pick the ones that are least invasive and have a good risk benefit ratio. You need balance to your face so I would recommend to start with a rhinoplasty. This will take the observers eye off your forehead and lips and is a predictable procedure in the hands of a surgeon that performs this kind of rhinoplasty regularly.

A few thoughts come to mind. You can meet with an orthodontist to assess your overbite and see if braces would correct that. If the overbite is too big for braces you could explore having orthognathic surgery to realign your mandible and maxilla (jaws). As far as your midface goes, a rhinoplasty with a rib cartilage graft to add volume to the Dorsum (top) of your nose will project your midface and allow for greater facial balance. Best