From the pictures it looks like an awful nice "parts gun"..... Yes the trigger guard and floor plate are wrong since they are milled and belonged to a M1903 not a late M1903-A3. The correct parts are available and not very expensive, the parts currently on the rifle are much more costly.
The real experts will be here soon and will give you more advise.
Meantime take more closeup pictures of the rifle and post them to help with the assessment.

D.