I’m on mobile so it’s lil hard to see the images, but, it doesn’t look like the armature is lined up quite perfectly. Like for instance there’s no thumb bones in the thumbs.
That alone shouldn’t mess things up too badly, but I can think of two other possible problems.
The first is that blender automatic weights usually do a shit job with meshes that are made of multiple elements.
The second is that perhaps all the vertex groups are still on the mixamo mesh from before, and they’re interfering. I don’t think that should be happening because mixamo usually names their bones differently. But it’s worth a check.
Are you just doing this as an exercise to practice rigging? If so you could just fix the weights manually, since that’s what you’ll usually end up doing while rigging unfortunately.
If you need the model done and functional for some other reason, I’d recommend just using the mixamo rig, everything is already set up perfectly, and you can just add IK if you need it.
I would suspect that it has other modifiers, and so your first pic isn’t it’s real rest position. Probably another armature. Would need to see the file to say for sure.
This really is a learning project both in rigging and then using the model and rig to learn how to do character animation. I think I’m going to have to end up fixing the weights manually, do you have a good reference on how to do that, as I have never done that before?
You need to line your bones up in edit mode, not pose mode. Clear all your rotations and scale, (alt G,S,R) before you begin on your mesh and your armature. Align your Armature with the mesh in edit mode not pose mode. Take a look at the Humane Rigging series. You can find it on you tube.