My guess is that one of your shift/ctrl/alt keys has “stuck”
This can happen when the OS gets the key-down event, but misses the key-up, so it thinks it still being held.
It happens to me often when using Alt+LMB instead of MMB to rotate the view - if I release Alt before LMB then the OS doesn’t notice and then any keys I press after that it thinks I’m still holding Alt.
Just press each shift/ctrl/alt key once each, and then it should fix it.
This would explain the box-select problem, if your Alt key was stuck then your computer would think you’re pressing Alt+B, which is an edge-select combo.
For the snapping, I’m not really sure. What it might be is that you’ve zoomed out too far, and the main grid is a lot smaller than the one you can see.