There are indeed different varieties of sorrel,* but they're both/all high (though I can't determine how high) in the substance of concern, which is oxalic acid. This acid is found in lots of other green leafy vegetables, notably spinach and parsley, and is the reason that you shouldn't eat rhubarb leaves.**
It seems to have a reasonably high expected lethal dose; the internet echo chamber puts it at 600 mg/kg, which would mean eating pounds and pounds of whatever leaf you've got. The necessary amount to cause sickness is obviously much lower, however. There's also a long-term risk for kidney stones -- oxalic acid combines or reacts with calcium to form calcium oxalate, which is a major component of those stones (and this is the mechanism for more immediate poisoning, whether lethal or not). I have also seen reports of simple mouth and digestive irritation, again caused by the calcium salt.
Unfortunately, it seems that cooking does not destroy oxalic acid. It may be possible to reduce its presence by boiling and discarding the water, however. It's unclear to me whether this is because the acid itself dissolves into the water, or whether the oxalates (Harold McGee says that the potassium and sodium salts are water-soluble) form during cooking and are dissolved.
In all, I think the only recommendation that can be made is simple moderation. It's incredibly unlikely that you'll kill anyone with a salad, but don't eat the stuff in large amounts every day.
*"Common" (looks like elongated spinach) and "wood" (looks a bit like clover, but the leaves are cardiod) are the two that I'm most familiar with.
**Although it seems that there's possibly at least one other poisonous substance in the leaves.
Unless you are using a canning method that is actually designed for long term storage and shelf stability, you cannot assume the food is sterilized or pasteurized by home processing methods.
You should therefore not expect a refrigerated shelf life of more than 2-3 days, the same as if you had not processed it.
Finally, you are creating a low acid food with absolutely no protection (other than refrigeration) against botulism, so you definitely do not want to store it more than this guideline.
In addition to botulism which is not detectable by odor or taste, if you do see unusual appearance, especially bubbling, or detect an off odor or flavor, you should definitely discard.
Best Answer
For the first part, about pouring hot soup in mason jars, it should be safe, but there's always a risk of shattering if the liquid is too hot.
There are many somewhat related topics regarding putting hot liquid in mason jars.
Is it safe to put fresh hot soup in a glass mason jar?
https://www.reddit.com/r/NoStupidQuestions/comments/9rd3y2/will_a_mason_jar_explode_if_i_put_it_into_boiling/
https://www.quora.com/Will-a-mason-jar-shatter-if-I-pour-hot-water-in-it ...
For the second part, It will not keep the soup hot/warm for a long time, it is not a "thermos" container.