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The leaf stem on overly sized leaves may be cut to the base if needed. Do not cut the woody-like stem of the plant itself. If there are any leaves that need to be removed from the woody stem, simply prune out the leaf tips instead, rather than the whole stem.

As long as the rest of the plant look fine and the roots are still intact, then it should be fine and continue to produce. You can remove the damaged leaves but treat the plant with neem oil to guard against pest or fungal problems. This article should help with the groundhogs: https://www.gardeningknowhow.com/plant-problems/pests/animals/get-rid-groundhogs.htm

If you are getting plenty of flowers but nothing produces, then it is most likely due to poor pollination. Hand pollination often helps. Here is more information: https://www.gardeningknowhow.com/garden-how-to/beneficial/insect-pollination-process.htm
https://www.gardeningknowhow.com/edible/vegetables/squash/pollinate-squash-by-hand.htm

If you have blossoms with some that seem to drop off, then it could simply be due to the fact that these plants will produce mostly male (non-fruiting) blossoms early in the season and will gradually start to produce more female blossoms as the season progresses.

This is typical behavior for curbit plants (squash, cucumber, melon). They will produce mostly male (non-fruiting) blossoms early in the season and will gradually start to produce more female blossoms as the season progresses. Give it some time and you will see it start fruiting. Here is how to tell a male from a female blossom: https://www.gardeningknowhow.com/edible/vegetables/squash/female-male-squash-blossoms.htm

This is sometimes referred to as twin or double fruitng. While not common, it does happen now and then. It's a condition where two or more blossoms, in this case female, fuse together and the fruit essentially grows as a siamese twin fruit.