DD didn't have full pincer grasp until 7-8 months, but she self-fed just fine before then. That's what the "handle" or "chip-shaped" pieces are about, so she could grab them in her fist and gnaw on the ends.
She also couldn't open her fist to get at what was inside yet. That's another development that comes later.
Personally, I feel that "pincer grasp" isn't the strong "sign" of readiness for solids that many people do. The pincer grasp is only about the ability to pick up tiny objects with thumb and forefinger -- that's not necessary IMO for eating. If they have the ability to grab an object and deliberately bring it to their mouth, that's all they need.
As for teeth -- DD didn't have any teeth until 8mo (then got 6 teeth in 6 weeks -- and no more since then!). She doesn't eat much differently now than she did then. The only real difference is that she now takes deliberate ripping bites of larger things, like pancakes. But even before the teeth she ate pancakes just fine. Those gums are hard!! Most 'chewing' is done with the gums at this age anyway, the true chewing teeth (molars) don't come in until much later. The "biting" teeth, the incisors, are useful, but not necessary for most solids.
About salt/no salt. We already eat reduced salt due to my HBP. So I don't worry about it TOO much. Foods with 'usual' salt amounts in them (ie, my reduced amounts), like breads and curries, I don't do anything different. Foods that would often be served with "extra" or "added" salt, like french fries or scrambled eggs, I cook up plain then everyone salts their own. I don't automatically add salt to boiling water, things like that, but I didn't before either.
Regarding sugar: I'm not going to stress about sugar. Glucose is an essential part of the body's energy system. Refined white sugar and processed sugars (HFCS) and artificial sugars are a different story, of course. But just because something is sweet does not mean it's BAD. Humans have a sweet tooth for a biological reason
That doesn't mean I'm loading DD up on cake and cookies lol... She eats a varied diet. But I'm not one who obsesses over sugar. I should add that I only buy 'natural' sugars, unbleached organic or sucanat, that sort of thing, I try to limit the amount of PROCESSED sugars in other words.