DS2 is my third DC, and at 16 months every meal is a nightmare.
He will not eat any finger food unless its bone dry like toast / dry breakfast cereal / rice cakes / crackers / bread sticks. He will not even eat cake or ice cream and he will not touch toast if anything is spread on it. He will not eat bread. He will not eat any fruit other than raisins (unless pureed).
I can just about get him to eat 2 meals a day or pureed meat / fish provided I add lots of butternut squash and sweet potato and "force feed". He spits out any lumps and every mouthful is a nightmare - eg trying to sneak it in when he is distracted by something, I even dance for him to make him smile and then sneak a mouthful in. He covers his mouth with his hand or "kisses" the highchair so I can't feed him. I know he'd happily eat cheerios/weetos at every meal, but I want him to eat better than this.
I avoid giving snacks as then he is even less hungry at mealtimes and its impossible to get anything into him at all.
He generally eats at the same time as us or at least as DD (7) and DS1 (5) but unless they are having cottage pie or similar he eats different food. I always put some of their food on his tray - he throws on the floor. Generally he eats best with a tray covered in toys (ie distracted).
He does only have 4 teeth so not that worried about the lack of lumps (and DS1 had a gag reflex that he eventually got over). But this is not a gag reflex, more that he just doesn't want to eat what I offer.
I should add that he is happy to eat the Ella's kitchen fruit pouches (and some of the veggies ones but not all) - he sucks them straight from the pouch without any fuss, but they are expensive, keep this more for if we are out for the day etc. He is also happy to eat smooth yoghurt and fromage frais. He likes some odd things - popcorn, sunflower seeds, edemane beans. He also loves chocolate but he very limited access.
He has 2 bottles of milk a day - one in the morning (I could drop this and he might eat breakfast, but he eats dry cheerios so sort of think that milk and then cheerios is ok breakfast and I might not do better if I drop the milk) and one at bedtime. If he has the milk from a beaker he only drinks 3oz instead of 6oz, will probably do that for the morning milk soon anyway.
Based on all of this, he is getting a balanced diet, but will he grow out of this behaviour (has been same since weaning at 6 months, tried at 5 months but he wasn't interested at all).