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They have blossom end rot. This article will help with that: https://www.gardeningknowhow.com/edible/vegetables/tomato/tomato-blossom-rot.htm

If it's not covering too much of the fruit, then simply cut it away and eat.

It sounds like you have tomato pinworm. If you accidentally ate one, you should be fine.

This article will have more information about them:
http://www.ipm.ucdavis.edu/PMG/r783300411.html

This is called cracking. In mild cases, like yours, the skin cracks as the tomatoes grow and heals over. It is safe to eat. In more severe cases, the tomato will split open. This article will help:
https://www.gardeningknowhow.com/edible/vegetables/tomato/tomato-cracking.htm

Yes, they will still be edible provided they're growing in an area free of chemicals or other issues.

Cherry tomatoes do mostly grow in clusters, but the clusters may be straight lines (like the vine ripe) or more circularly shaped clusters where the fruit stems come out from a central location on the branch.

The weather could very well be the problem. When temps are above 85 F, tomatoes slow in ripening. When temps are 95 F or higher, tomatoes can stop ripening all together. Many parts of the country are experiencing high heat, and if you are as well, this could cause the tomatoes to either ripen unevenly or stop ripening all together. It should correct itself when the temps come down. In the meantime, if you are afraid they will either die or you simply cannot wait, you can keep them on a window sill in a sunny location, or for an even faster way, put them in a brown paper bag. Here is more info: https://www.gardeningknowhow.com/edible/vegetables/tomato/how-to-turn-green-tomatoes-red-how-to-store-tomatoes-in-the-fall.htm

As for the splitting, this is called cracking. This article will help:
https://www.gardeningknowhow.com/edible/vegetables/tomato/tomato-cracking.htm