Sec, those are definitely not Watermelons, at least what I can see unless something is hiding.
Watermelon leaves have that greyish green color to them. Watermelon leaves are USUALLY about less than half the size of pumpkin leaves. Watermelon leaves have a SHAPE TO THE EDGES. Like a very wide oak tree leaf, or like some philodendron leaves.
http://www.whataboutwatermelon.com/index.php/tag/leaves/
About halfway down this website is a side by side photo of watermelon and pumpkin leaves. Course, different varieties of each look a bit different, but that's a pretty good photo. Or Sec, you could google up WATERMELON LEAVES, click enter, and then click images.
Moon and Stars watermelon varieties have naturally yellow spotted leaves, kind of variegated. Some of the yellow skinned watermelons do too, but with even more yellowness in the variegation. Some of the heirloom watermelons have very green leaves, and some others have almost sandy barely green grey leaf color.
Some Pumpkin varieties have huge leaves! Other Pumpkin varieties can have leaves just a bit larger than watermelon leaves. Most all pumpkin leaves are not the softest things. They have prickles along the midvein and other places, some varieties more than others. Watermelon leaves are generally much softer, some varieties are soft as charmin tissue, others might have some prickliness.
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Sec, what problems are you having getting things started? Being able to be specific about the conditions and things are not easy things to do at first. Like, talking to the OLE GARDENER DOWN THE STREET. He'll have a hard time helping you if you have a hard time describing things you did. Little things that seem like they would not matter sometimes do after all. For example, if your seedling flat was nice and warm in the afternoons when you check on it, but at night time it maybe almost actually freezes in the porch.
Digit has starting seeds indoors down to an art, but you'll see that we each have our own ways and timings.
That thing about pre moistening the soil mix to my mind does not seem important, so, years ago, I had to find out the hard way that it really is important. That's just one of the things. ohhhhhhhhhhhhhhh, how dumb i have been! me! I had to find out about damping off not once, but twice! I'm so dumb!!! So, I try hard to make sure others learn from my dumb slow learning mistakes.
Another one, it just did not seem to make sense: Compost must be done or else it CAN VERY WELL BE WORSE THAN HAVING NO COMPOST. Because, not finished compost is still growing with organisms that are ACTIVELY EATING THE SAME NUTRIENTS PLANTS WANT. So I learned that one twice also. Oh, I did also learn ways to kind of shortcut composting, but it requires a good amount of bone meal over the almost composted compost layer, followed by another layer of extra rich soil...that's a not recommended thing to do unless you either experiment on it, or have that old neighbor gardener carefully watch and suggest. But, im so dumb and had to do that mistake twice. One silver lining though: I hope I can show and explain my old mistakes so a younger and newer gardener might not do my old mistakes, or maybe only do them once.
Also, I hear tell yall on the east coast had strange weather this year. (((Global warming, polar ice cap melting, new shipping lanes that cruise to 100 miles of the north pole, the polar vortes, that's the jet stream that circles the earth north of the arctic circle, is weakening and that allows the colder arctic air to plunge south at some places, while allowing warmer temperate air to enter the polar region...something about the albedo of melted water soaking up heat much more that ice and causing more evaporation, and that decreases that polar vortex jet stream up there to reduce more...and that allows polar cold down the latitudes while allowing temperate air up there....badeep baddeep)
So, us gardeners...we sure are a determined and persistent bunch! Myself, next year I do plan on doing a couple new tepary bean projects in addition to more varieties of regular beans. Tepary beans may well be the kind of bean for the future globally warmed world...post holocene...
Even if not man caused, our planet does change basic weather patterns. There have been periods when the tropical regions were too hot for most life. I think that was the late permian. There have been periods when planet earth's ice caps extended nearly to the equator. I think that was the late devonian. (Someone correct me, but wikipedia has some excellent articles about geographic periods). So, we humans are well evolved and suited for this holocene period of warm mild weather. It can well get much hotter, or much colder.
Gardeners should be ready for it either way, and man made or caused or not, the reality of the reason doesn't matter. I as an individual of no consequence can do nothing about it. Tepary beans can grow in globally warmed and drought conditions. May as well begin diversifying, making new varieties of tepary beans. They need an easier to harvest variety, larger seeds, perhaps a snap bean variety or type of them.
Sorry, i start mumbling to myself...