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It may have too much nitrogen which can prevent flowering. You can try giving it some phosphorous rich fertilizer to offset the nitrogen.

Uneven watering or temperatures are normally the cause of fruit split in plants. Stem split is also common and usually due to extreme temperatures changes and uneven watering as well, but it never hurts to check for signs of pests, especially since they can penetrate the plant through these splits.

If you feel you need to go ahead and pick them, they will ripen off the vine. This article will help you:
https://www.gardeningknowhow.com/edible/vegetables/squash/ripening-green-unripe-squash.htm

You may have vine borers. This article will help:
https://www.gardeningknowhow.com/edible/vegetables/squash/squash-pests-identifying-and-preventing-squash-vine-borer.htm

You can eat the fruit, but you may find it is rather bitter or flavorless.

The most common reason for bitterness or bad flavor is stress to the plant. Too much heat, too little water or uneven watering are the most common reasons for this stress.

After you finish picking butternut squash, it needs to be cured. All that means is that you have to let the squash sit at room temperature for a week or two to fully harden the skin. They’ll need a temperature of about 70 degrees F., but don’t leave them outdoors where they’ll be vulnerable to insects.

Once cured, the fruit should be stored in a cool dry place (40-50 F.) such as a basement or garage. Do not let them freeze. Properly stored, your butternut squash should last from three to six months.

No, you don't need to give up. This article can help with the blossom rot issue: https://www.gardeningknowhow.com/edible/vegetables/squash/squash-blossom-end-rot-causes-and-treatment.htm