In the first sentence you wrote, you use there is because the answer is read as

Yes, there is some juice in the fridge.

In the second sentence you wrote, you use there are because the answer read as

Yes, there are some towels in the closet.

To notice that juices can have a meaning different from juice, as juices is used also to refer to the liquid that comes out from the meat when it is cooked, or the fluid secreted from the body (e.g., the stomach).

In the first sentence you wrote, you use there is because the answer is read as

Yes, there is some juice in the fridge.

In the second sentence you wrote, you use there are because the answer read as

Yes, there are some towels in the closet.

I use there're when I write, and the spell checker doesn't mark it as not correct. In some cases, when I use a contraction, the spell checkers underlines it in green, and it reports me that the word could not match the rest of the sentence; I think it happens when the contraction is used for different words, and the spell checker is not able to understand what I mean.

To notice that juices can have a meaning different from juice, as juices is used also to refer to the liquid that comes out from the meat when it is cooked, or the fluid secreted from the body (e.g., the stomach).