Yes, you want the cheato submerged, and it can go in your LR
chamber...... Now, no offense, but if I read that correctly, you are running your sump bass-ackwards. If you compare your sump to the workings of a canister filter, you want the input water to come through a filter sock, which acts as the rough sponge, then dropping into the equipment chamber where the skimmer acts like the filter floss, THEN the clean water goes into the LR
chamber, which is your biological media. The way you have it run, all the rough detritus is passing over & through the biological media first...... which is going to settle, rot, & nitrify.