Turbocompressors were mounted on top of some of the engines. On the B707-300, #2,3,4 has T/C. On the 707-100 and 720 T/C are on #2 and 3. There were other T/C permutations as I am
sure some folk will point out. The intake for the T/C was directly in front of the T/C hence the hole and the blunt fairing appearance. On non T/C fitted engines the fairing went down to just aft of the Nose Cowl.
The cowl for the T/C is called the 'Dog Kennel' and could be fiddly to fit (shoot bolt latches that required a boot to 'assist location' sometimes)
The vents are called Secondary Air Inlet Doors and are sprung loaded shut. They open at High Power seetings to allow additional air into the engines. Some JT3 had large inlet doors and some had narrower ones. The narrower doors were normally found on the 720 and 100 series 707.
I hope this info helps and I feel sure that others will provide a more detailed response. Anyone, please feel free to correct anything I have said as I have not worked on or been near a B707/720 for many years and the memory is now a little unclear.
Temps