The compressor delay is very easy to install. Since it says 18-288 VAC it can be installed in the thermostat line. Where? Just about anywhere. Inside or outside. They generally need a little bit of a heatsink.
Th load side is the side toward the relay. It doesn't matter which wire to the relay is interrupted.
The short cycle relay protects your fuse and/or breaker when the power or the stat is turned on and off quickly. In electronic stats, this delay is usually built in. In the mechanical stats it was easy to destroy a fuse block when a short power fail occurred. It helps your compressor too.