That is called catfacing - lots of discussions here about it that you can read through. It is basically weather related at the time of pollination.

Dave

Here is a link that might be useful: Catfacing discussions

Have you had some cool nights? I think that is a contributing factor. It is not attractive but shouldn't affect the taste.

Later fruit should be fine.

They are not growing well if they are deformed and the leaves are all curled up and twisted like in your pictures.
Looks like you have a viral disease

I don't see any signs of a viral disease, but it does look like hornworms have been munching on the plant in the first photo.

The leaf roll could be too much water, too little water, or even the stress of the heavy fruit load. Unfortunately it does make it easier for the hornworms to hide: their pale stripes look just like the veins on the rolled leaves.

When in doubt about hornworms, wait until it gets dark and take a handheld blacklight out and scan the plants with it. Hornworms fluoresce under blacklight just like scorpions. Makes them easy to pick out when they're literally glowing in the dark.