So I checked my booster and I have both of the ins and outs wired the same way. Does that mean I messed up the tip and sleeve on both? Can someone describe the differences, please? I have the middle tab on each wired to the tip and the tab to the furthest tab soldered to the sleeve. Correct? Wrong?
Wrong, as Stephen has explained. Switch them.
As far as telling the difference between them, if you closely examine the stereo jacks you're using, you can trace the parts of the jack that those solder tabs attach to. The middle tab is obvious--it connects to the tubular section that the cable tip inserts through, which is the SLEEVE (very aptly named, when you think about it). The TIP is the longer of the two bent "fingers" extending from the jack body, and you can trace it's base around to the solder tab that is located diametrically across from it. The remaining tab connects to the shorter "finger", which is the RING.
The op-amp pins don't need to be cut off. Normally you would bend them over to first make a good physical connection between them and the solder pad before you solder them together.
But just to clarify further, it won't hurt anything to trim the excess opamp leads down to the tops of their respective solder joints. Matter of personal preference. If you leave them as is, just be sure that they don't touch anything conductive, if you mount the PCB into an enclosure of some type.