Ron,
You ask some good questions.
A lower impedance 1:1 modulation transformer will have less turns, and a higher impedance 1:1 modulation transformer will have more turns.
So if you go much higher in impedance than the design center, you will suffer high frequency loss from all the winding capacitance, and if you go too low in impedance the low frequencies will saturate the core unless you roll them off at a lower level stage. Edit: I think I got this at least half right, but the more I think about it the more I get turned around.
With that 1:1 tranny you can effectively vary the turns ratio by staggering the modulator B+ from the RF AMP B+. So the tranny being 1:1 can be versatile. Keep in mind that modulation transformers typically don't have a lot of insulation between the primary and secondary windings.
Also this thread pasted below needs a good re-read:
http://amfone.net/Amforum/index.php?topic=27244.msg207633;topicseen#msg20763373,
Jim
WD5JKO