Hey - nice bike.
The tube under the tank was put there because of the way the tank fits over the upper frame tube. Unlike the tanks on much later bikes, the early twins' tanks have sides that sorta hang over the tube (you'll see when you take the tank off the bike) and without the tube, you can end up with a quarter of the tank of fuel you can't use 'cos it can't get from one side to the other - unless you lean the bike a long way over to one side.
I've got an SL350 and a CB450 and have given up trying to disconnect that tube with fuel in the tanks - no matter how careful you are, you'll spill some. Easiest thing to do is this: as soon as you walk into your workshop/garage, get two long-ish bits of tubing with a diameter slightly larger than that of the fuel tubes and a plastic fuel can. Make sure the fuel tap on the bike is set to 'off' and disconnect the fuel tubes from the carbs. Put the fuel tubes into the larger tubes and the ends of those tubes into the fuel can which should be on the floor next to the bike. Turn the fuel tap onto reserve and let the fuel drain while you get on and do something else (making sure the can doesn't overfill. The tank'll be empty before you know it, and you can get it off cleanly. And once it's off, you can give it a good look over inside, and pull, check over and clean the petcock filters that live inside the tank. When you're done, put it all back together and pour the fuel back in.
With a CL, chances are you won't be able to get at the left hand air filter without the exhaust coming off. It's a PITA, but it's not that hard to do. Refitting the filters is very difficult if the rubbers that mount on the connecting tube (parts #2) come off with the filters. Don't try to remount the filters without taking the rubbers off the filters and mounting them to the connecting tube first. Sounds simple (it is), but it's a real tough job trying to mount them up with the rubbers attached to the air filters.
As for the connecting rod you're looking for, you'll end up spending way more than you need to if you want an original part. If you're not too fussy about originality, get down to a hardware store and pick up some threaded rod and either dome nuts or nylocks, together with a couple of rubber and penny washers. Cut the rod to the right length - you may find the part number gives the correct length 'cos the SL350 part number is 92000-06238, with the 06 meaning it's an 6mm (M6) rod that's 238mm long. Once the rod's in the right place, put a rubber washer on each end, then the penny washer, then the nuts on the outsides. That lot will do the job real well, and will cost a fraction of the original parts.
Hope some of that helps.