I just let 3 gallons of cider ferment for about a month now. I thought that campden tablets would kill my yeast and I could back sweeten with some juice. But from reading that I was wrong. Please help?
Campden (potassium metabisulfite) will not kill yeast. That is why winemakers use it.
Sorbate doesn't kill yeast, either, but it inhibits yeast reproduction.
This is from the "beginning cider" sticky here:
https://www.homebrewtalk.com/showthread.php?t=508303 You may find it helpful.
Sweetening the Cider:
If the cider is finished, and clear, then campden and sorbate will allow you to sweeten the cider. If it's not finished and there are a lot of lees (sediment), it won't do anything.
The way it works is that sorbate does not kill yeast, but it prevents yeast reproduction. So, in an active fermentation when there are hundreds and hundreds of billions of active yeast, it won't do a thing. But once fermentation stops, and the cider clears, and the cider is racked off of the fallen yeast, it can be added to prevent yeast reproducing, thereby not allowing fermentation to begin again (usually). Sorbate works better in the presence of sulfite (campden), so they are generally added together.
However, it will NOT stop an active fermentation and will not work in a cider that is not clear and done fermenting.
If you use this method, and it is successful, you can sweeten to taste without any risk of bottle bombs.
Because the yeast has been inhibited, however, you will not be able to bottle carbonate the cider. Carbonation is a function of the yeast.
It's fairly easy to make a sweet still cider, or a dry carbonated cider. To make a sweet sparkling cider, extra steps and techniques like bottle pasteurization or kegging would be needed.