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String works, like you would herbs. You can also place them in mesh bags and hang the bags. The point is to make sure there is good air circulation around them.

Transplant geraniums in spring after all danger of frost is over in your area. If plants have a heavy, dense root ball, break up the root ball before planting. Plant geraniums at the same level as they were growing in pots or the garden.

Most likely it is overwatering. Geraniums like to by dry. Water only when the soil is dry to the touch.

Give it some bone meal to balance the phosphorous back out and that should help bring the blooms back. Cut off about 1/3 to 1/2 of the woody stems on the plant to help get rid of the legginess and encourage new, green growth.

Yes, you can. There are several way to winter geraniums. This article will help: https://www.gardeningknowhow.com/ornamental/flowers/geranium/how-to-save-geraniums-over-the-winter.htm

Your husband is correct. Placing dirt over the roots can smother them and kill the tree. Consider planting the geraniums in pots that you can place around the base of the tree.

Without a picture, it would be hard to identify it. But perhaps this is it: http://bugguide.net/node/view/220119

Regardless, all caterpillars are treated the same way: https://www.gardeningknowhow.com/plant-problems/pests/insects/prevent-caterpillars.htm