I try to grow melons (ex. cantaloupe, watermelons, pumpkins, gourds). Sometimes I will have twenty (20) blooms on a plant, but then the bloom will begin to wilt and fall off, just like you take a knife and cut it off. The plant stays healthy and may produce 1 or 2 melons. Can you shed some light on what the problem may be? Thank you.
This is actually normal behavior. As with squash plants, melons and pumpkins produce more male flowers early in the season, which eventually drop off. Males do not produce fruit. Given a little time and patience, your plants should begin putting out female blooms and you will begin to see some fruiting.
Should I pinch the melon vines to stop the vine growth, or leave them alone and let them continue to grow out? And, related to that question . . . What about pinching off flowers? Does that help or hinder?
While you can pinch out the growing tips, regardless of how much you do this, the plant will still continue to grow out.
You can pinch back nearly any type of plant such as annual flowers, vegetables, herbs and late-blooming perennials. Plants that develop their other branches from the base of the plant can be pinched but isn't required and does not hinder nor help either way. Generally, pinching on some plants helps promote bushier growth and on others may encourage flowering. Here is more information:
https://www.gardeningknowhow.com/garden-how-to/info/pinching-plant.htm
My plants have done very well this year. I have tons of flowers on my tomatoes, melons, cucumbers, and zucchini but the only thing fruiting is the tomato. I've seen ants inside the blooms and just used a treatment on your site (cornmeal, cinnamon) for that but I'm not entirely convinced that is the sole issue. Something is eating on the zucchini leaves but I've not actually seen bugs. Any suggestions?
I would recommend you apply neem oil. It is used to manage over 200 other species of chewing or sucking insects so odds are you will be able to contain your culprit. More information on neem oil can be found here:
https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm
With regards to the ants - here is an article with additional things you can try:
https://www.gardeningknowhow.com/plant-problems/pests/insects/keeping-ants-off-flowers.htm
Can you trim (and how so) a muskmelon plant to increase fruit yield? We have a plant with 6 developing fruit near the base with a lot of flowers/very small fruit further down the vines but no sign of any of the distal fruit developing. Is there a trimming technique to stimulate more of the fruit to mature?
Yes, you can prune the vines.
Though the link below is about watermelon, the same technique will apply.
https://www.gardeningknowhow.com/edible/fruits/watermelon/cutting-watermelon-vines.htm
https://www.gardeningknowhow.com/edible/fruits/cantaloupe/growing-cantaloupe.htm
http://cals.arizona.edu/crops/soils/azncantaloupe.pdf
http://www.ipni.net/publication/bettercrops.nsf/0/4A87D50760EB9CA18525797D0061579A/$FILE/Better%20Crops%202011-1%20p13-15.pdf
When growing cantaloupes or other melons, should the small sucker vines be pulled off regularly?
Here is a link with information.
https://www.gardeningknowhow.com/edible/fruits/watermelon/cutting-watermelon-vines.htm
Want to locate pepino seeds.
I would recommend doing a local search for your area to find any retailers or even mail-order catalogs. Your local garden center may also be able to help. You can also check out eBay. In my experience, eBay is actually a great place to find unusual plants/seeds. Just check the feedback on the seller before you buy. There are many seed swapping garden forums that may offer the seeds as well.
I have this Christmas melon that was picked in October but sitting on my counter all this time. It was starting to liquefy on the bottom and it has furry white mold over most of it now. It is rotting, but could the seeds be saved safely?
Yes, you can save the seeds.
This link will help you.
https://www.gardeningknowhow.com/edible/fruits/melons/melon-seed-harvesting.htm
Keep in mind that since the Christmas Melon is a hybrid, the seeds will likely not be identical to the parent plant.