Hello & Welcome,
Since I cannot see exactly you will need to tell me what the part name is.Ask who ever is working on it.
No,do not try yo drive with an axle out.
All Right ,very good picture.Just from looking at the parts i am guessing that you the intermediate shaft housing & maybe a clutch sleeve.
If these parts are on back order ,I suggest (the only thing to do besides wait) is go to a salvage yard & purchase a front axle assembly.That is most likely the way they will want to sell it.