Refusal to eat is the most common sign of dental trouble. It’s not uncommon in aging bunnies (I don’t really want to call him aging, but he’s not a youngster so for lack of a better word. I don’t mean he’s geriatric), because the bones in the skull becomes less dense with age (for completely natural reasons), which may cause the jaws to become slightly misaligned, the teeth are not ground down as they should from eating and spurs form as a cosequence. rabbit teeth grow very fast, 1-5 mm per week, so if they’re not properly worn, a problem can become manifest after just a few weeks.
When my Yohio had his dental issues he would eat some things and not other, but I don’t remember if carrot was sth he would eat. He went off pellets and hay, that I remember though.
The vet will try and check your buns molars with an otoscope, that’s not the easiest thing to do with an awake bunny (obviously), but if there’s sth apparent, it can be spotted. An experienced bunny vet can also gently move the lower jaw from side to side to “hear” or “feel” how the teeth slide against each other.
The oddly shaped poops you see are probably due to too little hay. You don’t want it progressing into real tummy trouble, so it’s good that you’re seeing a vet.
And if your vet decides a tooth grind is warranted, ask for a pain-killer (metacam, meloxicam) that you can give at home afterwards, even if the teeth don’t have nerves, the gums are often sore after a burr/grind and the bunny may not want to eat for that reason.