It kind of sounds like the old T-45 bent fork problem that many GT owners have had. But yours is a T-5
tranny, and it should be a a stronger shifting mech design.
It could also be a clutch on the 1st gear issue, but that dosen't explain the reverse problem as well.
Not to sound stupid, but have you adjusted the clutch? If not, it's easy to do. Just slip you foot under the clutch pedal and pull up on the pedal hard. then press the clutch pedal all the way to the ground. It's a self adjusting clutch, sort of, but you have to help it along.
Also, I had a Mustang that was tough to get into reverse, not grinding but just didn't like to get into reverse at all. So, I would engage the clutch and then quickly slide the shifter into 3rd and then into reverse. Since 3rd is on the same gear ring as reverse, I think it seemed to align things up better.
Hope this helps,
Glen
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-1998 Black Cobra, Kenne Bell 2.1L Supercharged
-2005 Mustang GT, Premium, 5spd, Redfire, Mac Catback
-2007 Roush Nitemare Stage 3 Supercharged #48 of 100