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Yes, those appear to be male flower pods. Female flower buds will have an ovary at the bottom that will swell into the fruit once pollinated. Seeing male flowers first is a very common occurrence. Not to worry. Female flowers will show soon enough, with the right care.

This collection of articles will help you to grow pumpkins properly: https://www.gardeningknowhow.com/category/edible/vegetables/pumpkin

Golden Nugget pumpkins can keep for a couple of months if stored in a cool, dry place. They are a small, orange, spherical variety. The seed package recommended thinning to one seedling per hill.

https://www.gardeningknowhow.com/edible/vegetables/pumpkin/post-harvest-pumpkin-storage.htm

If these were seeds kept from a previous pumpkin, then it could be luck of the draw on genetics. This behavior will be quite normal in many squash varieties, and can present itself in pumpkin planted from a harvested crop, due to cross-pollination from other species nearby.

Try a fresh packet of pumpkin seeds from a trusted producer to ensure that the seeds will grow true. Once this test is done, and if the issue is still present, then you can chalk this up to a virus in the soil. Usually it does not cause "netting" this badly on pumpkins, though.

Most plant viral infection cannot be killed off. You will need to avoid plants susceptible to pumpkin viral infection if this is the case.

Here is an article that will provide some useful tips to gardening pumpkins:

https://www.gardeningknowhow.com/edible/vegetables/pumpkin/pumpkin-growing.htm

At the very least, a 5-10-5 is appropriate. The best thing is to add organic compost, periodically, to provide the best range of nutrients.

This article will offer more information: https://www.gardeningknowhow.com/edible/vegetables/pumpkin/feeding-pumpkin-plants.htm

The rain won't affect them, too much. As long as the curing time is mostly sunny, that is.

As long as there is no frost, you can leave them out in the rain.

I would definitely replant right away. A few nights of freezing temps definitely could have killed your seeds. Your soil should be in the 60 degree temperature range when you plant, so new seeds are probably in order.

https://www.gardeningknowhow.com/edible/vegetables/pumpkin/pumpkin-growing.htm