Can the SK1215 handle set replace all look alike handles?

The short answer is NO.

Some manufacturers have handles that look like our SK1215, but aren't compatible.
Ideal's SK1215 handle has only 2 screw posts, whereas many other look-alike brands have 4. This makes them un-compatible. 
Also the center distance of the lever to the bottom key hole is 3.715” on Ideal's SK1215.   
Check out the instruction of the SK1215 for detail dimensions.
If you have four posts handle sets, check out the BK1216.