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The following article(s) should be of some help to you: https://www.gardeningknowhow.com/edible/fruits/watermelon/growing-watermelon.htm

Typically, watermelons can remain on the ground without any problems; however, many people prefer to place the young melon on a piece wood (piece of plywood, 2x10, etc.) to keep it off the ground, where in some locations or overly wet conditions, the melons can be susceptible to pests or rotting. Please let us know if you have any other gardening questions.

This is normally caused by irregular watering. Usually too much at first and then not enough as they are reaching maturity.

This article may be of some help:

https://www.gardeningknowhow.com/edible/fruits/watermelon/growing-watermelon.htm

Yes, you can prune back watermelon, or you can grow them on a sturdy trellis, please see these articles for more information on growing and pruning.

https://www.gardeningknowhow.com/edible/fruits/watermelon/growing-watermelon.htm

Watermelons are heavy feeders, so make sure the area in which you plant them is rich in organic materials. Normally, you only thin them if you are looking to grow a big melon. Do it after the melons have formed. Keep the strongest, largest one. Water deeply and side dress with compost.
This article should be helpful:

https://www.gardeningknowhow.com/edible/fruits/watermelon/growing-watermelon.htm

The only blossoms you will need to trim to do this are the female blossoms. Female blossoms will be sitting on a small, immature fruit, while male blossoms will simply be sitting on the stem. Male blossoms will not produce fruit. Select a few female blossoms that you would like to keep (try to keep them spaced out on the plant) and then use a sharp pair of scissors to trim off the rest. Just snip them right behind the immature fruit.