When you go Wide Ope Throttle, most cars will richen the mixture to be on the safe side. You can get a mixture as rich as 9:1, as I have seen on some cars.
You make more power the "leaner" you go. So, get the mixture away from 9:1. There are a lot of variables, but the usual sweet spot for direct injection cars is around 12:1. Any leaner, you get detonation/knocking. You can help this by running higher octane, water/meth, etc.
If you are seeing 11-12 when flooring it, that is a normal AFR for flooring it. Cruising and idling should be 14.7:1. Partial acceleration AFRs vary widely depending on throttle input, boost pressure, temp, etc.
When you get a tune, there are many, many parameters in the computer to adjust and optimize. Making more power with a tune is an adjustment of these parameters including "leaning" out the AFRs to an acceptable level. Tuners will adjust AFR, ignition timing, and many other parameters to make more power for you.
In these many parameters you can also optimize gas mileage by adjusting the appropriate tables. Once I get into tuning, I can post how some of this works.