So this is me shooting in the dark, as I havent looked at the file as it would be a while until I can. But someone informed me a bit about the file.
From what ive read and been told, it sounds like all of the joints are world aligned in the mixamo t pose yeah? Usually that wont work. Mixamo when it first started, used this world alignment, but down the road they switched to a Y down the bone alignment. But there are still some animations and or characters without this new alignment. The 21 mixamo rig will not properly retarget those that are world aligned.
As someone else mentioned, you should delete everything but the model and re rig it through mixamo and apply anims there. That should probably generate something for you with the proper alignment.
Like Orestis saidd if the knees bend backwards its probably just because of how mixamo chose to place the joints. Sometimes because of the model it can make it so the knee joint is ever so slightly behind the thigh or ankle. When this happens, the knees will bend the same way. So jump back to adjust mode and after they snap back, just hold the move without child key to drag the knees a little bit forward so they are in front of both the thigh and ankle.
Also if you choose to not have the mixamorig: namespace, a lot of the helpful automatic features will not work for you. The auto adjusting, retargetting buttons and weight transfer stuff might not work automatically, but you can still manually do each step(ie turn on axis locking to snap during adjust, manually dragging and dropping the necessary joints into their corresponding retarget slot etc).
Hope this helps