In theThis morning, I tried to make a carrot juice.

Unfortunately, while iI was makeing it, the hand blender was broken.

I don't like carrots so I wanted to grind (blend?) all the carrots but half of them wredidn't ground.ind (blend?)

I could chew all the chunks of carrotarrot chunks.

In the morning, I tried to make a carrot juice.

"A carrot juice" is not unheard of, but in that situation, there is implicitly an omitted classifier (like "glass" or "type of"). Example: https://english.stackexchange.com/q/276491/113475 "Carrot juice" might also come more naturally to some people.

Unfortunately, while i make it,en I tried to make it, I found that the hand blender was broken.

When you use "while," the main clause should have an action that takes place during the time indicated by the "while" clause. "Was" and other forms of "be" can't be used here, because they describe ongoing states.

I don't like carrots so I wanted to grind up all the carrots, but half of them weren't ground still in large chunks.

I could chew all the chunks of carrot [in my carrot juice].

I would just say "chunks of carrot" unless you're trying to emphasize how much carrot you had to chew: "As I drank the juice, I had to chew all the chunks of carrot left."

In theThis morning, I tried to make a carrot juice.

Unfortunately, while ithe hand blender was broken. / Unfortunately, when I tried to make it, the hand blender was broken.

To me, "while I make it" seems redundant, but I would use the second sentence if you wanted to keep it in.

I don't like carrots so I wanted to grind all the carrots but half of them wren't grounblend them, but half of them did not get blended.

I couldhad to chew all the chunks of carrot.