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It depends on where you broke them and how completely they were broke. If the break happened further down the plant and there are plenty of leaves behind the break, then the plant will like grow branches and be fine. If the stem was bent rather than severed, straighten it out as best you can and it may recover. To help it further, bury the damaged part of the stem under some soil.

If the main stem was severed and there are few leaves behind where it was broken, then you may need to replace the plant.

Squash plants always produce male flowers first, female (with the fruit behind) will come in later. This article will help:
https://www.gardeningknowhow.com/edible/vegetables/squash/squash-blossoms-falling-off-vine.htm

Squash plants require plenty of light (full sun) and water (at least an inch weekly) throughout their growing season—watering with a soaker hose provides the best results, as this allows it to penetrate roots more easily rather than turning into runoff. This article should help you as well: https://www.gardeningknowhow.com/edible/vegetables/squash/how-to-grow-summer-squash.htm

Neem oil should help take care of the problem. Here is some information that may help: https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm

This is common with squash plants. They produce male flowers before female flowers to make sure that pollen is on hand when the female flowers show up. The female flowers should be coming soon. This article may help:
https://www.gardeningknowhow.com/edible/vegetables/squash/squash-blossoms-falling-off-vine.htm

It sounds like transplant shock. This article will help you:
https://www.gardeningknowhow.com/plant-problems/environmental/learn-how-to-avoid-and-repair-transplant-shock-in-plants.htm