No early A-body car came with dual exhaust and as such all of the transmission x-members are cut out on the drivers side only. In 1967 when the body change was made the x-member was reconfigured for a dual cutout as A body cars were starting to come with duals.
To answer your second question, no, a later x-member will not fit under an early A-body car. You need to do a dual cutout conversion to allow passage through the x-member.
Included is a couple pictures of the early A-body dual exhaust cutout conversion I was offering here for a while. I had about a dozen made but sold them all and haven't been able to amass any other x-members to do some more. I was selling them for $60.00 blasted and painted with the conversion done, and was offering a $10.00 discount if the buyer would ship me his unaltered core to continue this endeavor. Alas, I didn't receive a single core!!
Hope the pictures help!! Geof