Does fermented food leads to acid reflux and sore throat?

No. Acid reflux is physiologic. In other words, it's normal. However, it becomes pathologic when it bothers you. Fermented food doesn't cause acid reflux any more than non-fermented food. However, "bad" acid reflux allows acid to get high enough back up esophagus to cause sore throat. Antacids (calcium carbonate), H2 blockers & proton pump inhibitors help. Stay upright after small meals.
No. These types a food alone will not cause acid reflux, but if you already suffer from this problem certain types of foods can make the symptoms worse.