Hey Jhen, VIF and I have had great results with squash, particularly zucchini. The yellow squash is more finicky. Sevin dust, liquid or powder works great on all vegi's to keep the pests off.
As far as putting your extra squash outside the garden, no problem. Dig a gallon sized hole in your red clay. mix the removed soil with black cow manure or mushroom compost, or if you're in a pinch miracle grow soil will work. You have to mix it with the existing soil or the roots will not spread in the ground. You should have great luck! VIF and I have been working on our garden for many years. We have been retraining ourselves for Florida gardening.