In a nutshell you have a crucible KI that's tied to your character. It has elements stored in it that are used for fuel which you can refill yourself or pay an npc to do for you. You can place your crucible into any furnace. Once in a furnance you can either trade fuel to refil it yourself (fewells) or you could trade ingredients. Once you start a synth you basically feed it fewell of a certain element to try to match the target numbers. For example if your target number is (fire 10) you spam the feed fewell command for fire until you get as close as you can to (fire 10) before clicking to finish the synth. It doesn't have to be dead on but if it is you have a higher chance of HQ'ing.
There are alot of complications that can arise and it's alot more intuitive than in the simplified explanation I gave. To answer your question though, no you can never lose your ingredients. A method to skill up synergy fast involves taking a high lv recipe and purposely spamming fewell feeds till you fail since every action you take in synergy has a chance of a skill up. Hell you could trade ingredients to the furnace, fail the synth, log out, come back 3 days later, and you would still get your items back by clicking on any furnace again.