There are three burns or two burns used in landing.
It depends where they are landing. Downrange, they basically fly ballistically after MECO (landing on barge downrange) and do their first burn to survive re-entry through the thicker parts of the atmosphere when they are going fastest.
If they are doing an RTLS, (Return To Launch Site, land on land) they first do a boostback burn, that slows their forward velocity and starts them reversing direction back to the launch site. Then they do the above re-entry burn as needed.
Finally there is always a landing burn.
They have tested a number of different approaches.
Sometimes 1, sometimes 3 engines in each burn. It is dependent upon the mission specifics. They have tried 3-3-1, 3,3,3 and other combinations for landing as they experiment to determine the best landing options in different conditions.
The benefit of a 3 engine burn is reduced gravity losses. That is, you are falling at 9.8 m/s/s no matter happens. Every second longer you spend falling you are fighting gravity.
So if a 1 engine burn takes 15 seconds, but a 3 engine burn can do the same task in 5 seconds, you potentially used similar amounts of fuel but you have spent less time fighting gravity.
Or so the theory goes. Only 3 engines are plumbed with TEA-TEB onboard (rest are ignited by groundside equipment during launch. Actually I think all of them are to save TEA-TEB for landing, but you know what I mean). So only three can restart.
As for backflow, they clearly have figured out how to ignite them in the midst of landing flights and once an engine is going it has pretty strong thrust to overcome any back flow.