In FF14, equipping weapons is how you change your class. So when you equipped the Saw, your class changed to "Level 1 Carpenter" and all of the equipment that a Level 1 Carpenter can't wear was unequipped.
But don't worry, all of your items and their glamours are still there! By equipping your old weapon, you can become your combat class again, and then you can equip your old gear and be back to normal!
One thing you'll probably want to do once you figure that out is to save Gear Sets for your different classes; that way you can easily switch from being a Carpenter to being a different class without becoming naked and having to put on all your clothes one-by-one. Here's the official tutorial page on that:
https://na.finalfantasyxiv.com/uigui...pment_set.html
If I understand you correctly, you chosen to synthesize the item, which starts the process of synthesis, but you have yet to play the "mini-game" that you need to do to actually finish the synthesis. There's an explainer if you go to this page and then click the big "Disciplines of the Hand" button:
https://na.finalfantasyxiv.com/craft...ide/carpenter/
I hope this helps!