G’day again Keven now that you’ve posted pics people that know the boat can give you some tips to get on the water. Getting your cat looking about right is only the start and I would really urge you to join a club and sail there so that you have company, assistance, supervision and people interested in increasing your sailing skills. Don’t feel bad because you’ve got a rougher boat, you have to start somewhere and there will be others like you in the club, the main thing is you share the same interest in sailing. Only this weekend I re rigged and gave parts to a stranger who was sailing his new to him older cat for the first time without his centre board and didn’t have the bits or knowledge to lock it down, you will find people at your local club that will do the same for you.
I don’t know the Hobie 16 setup at all but most cats are similar so this is what I think.
Number 1
Those rudders lock in the upright position for launching etc so you need to lift the rudder crossbar and push back, if it’s stiff spray some lubricant into all the places where it needs to pivot. I use a Lanolin spray and you can use it on your sail tracks etc without staining your sails consider spraying a little bit on every place you have a shackle, pivot point or nut.
Number 2
The two single blocks shackle onto number 3 with the double block somehow attaching to the top of your traveller. The traveller is the bit that slides along your back beam in 5, if your main sheet is long enough it will go back through your traveller or you will need a separate sheet to go through your traveller.
Number 4
This is your vang this stops your boom from swinging upwards and bagging up your sail when you let too much main sheet out, without it your boom can swing wildly up and down in gusts . There will be a loop of steel or a shackle near the bottom of the mast where you would normally attach a block that goes to another block that attaches to the eyelet on the boom in the photo then goes to a V cleat or similar so you can adjust your settings. If you don’t have it with the boat and want it (I would) just tie some decent sheet there after you’ve rigged the boat and that will do for now.
Number 5
This is your traveller set up which your mainsheet double blocks need to somehow attach to the top of the sliding bit (the traveller) and not to the top of the cleat. The traveller sheet will go through the fixed eyelet near the tramp, be long enough to let the traveller go to the end of the beam then go through the traveller between the black rollers and back to the saddle on the back beam where you tie it off so when you pull the traveller sheet from the tramp it will pull the traveller to the centre. Once you have the main blocks setup you should be able to thread the loose end through that cleat on the traveller but some things not right with your set up and I think there should be another block in front of the cleat. (Will have to work on that hopefully someone else more knowledgeable will jump in here)
Number 6
Shackle or tie the bottom of the jib to where your bridle forms the V shape so that the jib is down low that way when you pull the jib halyard it will pull the jib tight. I think you should be pulling the halyard back to where you’ve attached the bottom of the jib and tying it off there or if the halyard is long enough going through a steel loop and back to the mast to tie off, pull it tight
Number 7
Pull the main sail halyard on real tight and it will stretch the sail upwards, is there a small steel V cleat or something up the mast to secure the top of the halyard? In photo 8 I see a block on the end of a halyard if that’s the end of your main sail halyard the halyard would go through another block then up through the block in the picture then pulled down tight to tie off where you are tying off now, pull really hard. Did you try to slide the bottom of the sail in the mast track before you put the boom on?

Trapeze setup
These shackle on to picture 9 which looks normal enough to me.

With lowering the mast if the mast base is pinned have your helper hold a trapeze handle in each hand and walk toward you as you walk back on the tramp then the helper goes to the back to hold the tip. If its not pinned tie a short length of rope joining the base of the mast to the beam so that no one can get hurt. Then have your helper hold the base of the mast down as you slowly walk backwards never have anyone underneath ready to catch the mast until they can reach it. Do it on the ground I wouldn't walk on your cat on a trailer or beach rollers you'll just wreck it more.