Right, basically whenever I try to move an audio clip, it jumps a full measure instead of increments, which drives me crazy. This results in it either creating an akward pause that I can't really leave in, or it results in the 'new' audio overwriting the old, because for SOME reason there's an option to rewrite old with new, but not vice-versa. When I try to 'stretch' it, this apperently brings back the old audio that I split off, so I have no idea how to actually fix this issue. Basically I would like to know how to move audio to certain time stamps instead of full measure increments.

Dragging clips is affected by snap settings http://www.cakewalk.com/Documentation?product=Music%20Creator%207&language=3&help=Arranging.25.html#1471004
 
Process > Nudge from the main menu (although I would recommend learning the keyboard shortcuts) moves clips and can be set to very small increments http://www.cakewalk.com/Documentation?product=Music%20Creator%207&language=3&help=Arranging.20.html
 
Another way to place a clip at a specific time is

• copy/cut the clip
• type G to bring up the Go dialog
• enter the time and click OK
• paste the clip