Will basil plants winter over indoors and at what point can seeds be planted?
Yes, basil can be grown indoors in the winter. Here is an article to help you:
https://www.gardeningknowhow.com/edible/herbs/basil/information-on-how-to-grow-basil-indoors.htm
If you will be growing basil indoors, the seeds can be started anytime. Here is an article to help:
https://www.gardeningknowhow.com/edible/herbs/basil/growing-basil-seeds.htm
Do I dig up my basil or cut back below leaves for winter?
Basil is a rather short lived annual. You can expect it only to survive the summer and after that it will get woody. It is best to start a new plant for winter to grow indoors (so, yes, you will need to grow it indoors for winter.)
Here are some articles to help you with your basil plant and future basil plants: https://www.gardeningknowhow.com/edible/herbs/basil/how-to-grow-basil-plants.htm
https://www.gardeningknowhow.com/edible/herbs/basil/growing-basil-seeds.htm
https://www.gardeningknowhow.com/edible/herbs/basil/propagating-basil.htm
https://www.gardeningknowhow.com/edible/herbs/basil/information-on-how-to-grow-basil-indoors.htm
I want to harvest the basil in my garden and store for use through the winter.
Here is an article or two that you may find helpful: https://www.gardeningknowhow.com/edible/herbs/hgen/freezing-herbs.htm
https://www.gardeningknowhow.com/edible/herbs/hgen/how-to-dry-herbs-various-methods.htm
I like to put the leaves in a papertoweland roll it up,then put it in a freezer plastic bag. when i need basil i pull out some leaves and they defrost quickly so i tear it up with my fingers. I put it in salads or pasta.some people put leaves in icecube trays and put water over them and freeze them.
you can make pesto and freeze it.
Something is eating my entire basil plant from the top up, leaving me with only a few bottom stalks. This is not a bug nibbling on the leaves but rather something (not a neighbor!) taking the entire plant. I planted new ones in a different area of the herb garden but the fresh plant nearest the older ones was eaten last night. Any clues?
The most common culprit for this is slugs. They love basil and can literally devour plants overnight. Read this article for some advice on getting rid of them: https://www.gardeningknowhow.com/plant-problems/pests/facts-about-slugs-and-how-to-kill-garden-slugs.htm
I am succesful in getting basil to germinate but once potted and the leaves are about an inch high, they fold over and stop growing. They are in a window sill and get lots of sunlight - what am I doing wrong, please?
I would recommend less water and when you do water, water the seedlings from below. It sounds like the seedlings are damping off, so a little fungicide in the soil will help as well. Here is more info: https://www.gardeningknowhow.com/garden-how-to/seeds/what-is-damping-off.htm
Two years ago I planted basil in a container and loved it. It went to seed and I now have flavorless basil growing all over my yard! I need to find a way to get make it go away.
Other than hand-pulling it all up, your only option would be to spot treat them with Roundup, which dissipates rather quickly.
I started growing basil but need to be away for two weeks. What sort of ways to give water necessary for basil to stay alive and grow while I am away?
If you do not have anyone that can keep them watered for you, there are self watering systems available that may help. This article has some additional suggestions: https://www.gardeningknowhow.com/houseplants/hpgen/while-youre-away-vacation-care-for-houseplants.htm