What is the halacha with regards to switching on an electric Shabbos urn close to Shabbos?

One is forbidden to put a pot of raw food or uncooked water on an open flame close to Shabbos, unless there is a sizable piece of meat in the pot, which will not be ready for the night meal. Since an electric urn does not incorporate a blech or hotplate it is considered an open flame. Therefore:

Sephardim must fully boil the water before Shabbos. [1]

There are, however, poskim [2] who hold that water cooked to the degree of yad soledes bo (40-45C) is considered fully cooked, and when there is not enough time before Shabbos to bring it to a boil, it is sufficient.

Ashkenazim have what to rely on and suffice when the water is cooked to the degree of yad soledes bo. [3] L'chatchila Ashkenazim should also fully boil the water before Shabbos. [4]

If boiling water was poured onto a tea bag, may one drink the tea?

The Mishna Berura [5] writes that pouring hot water from an urn directly onto tealeaves involves an issur Torah (a Torah prohibition), because one cooks the tealeaves and the tea is prohibited to imbibe.

How does one prepare tea essence before Shabbos?

The preferred method is to make tea essence before Shabbos by placing tealeaves/bags in a small kettle and cook them on the fire, or at least to pour boiling water onto the tealeaves/bags, stirring the leaves while pouring the water.

On Shabbos one pours hot water into a clean, dry cup and adds the tea essence to the water. [6] One need not keep the essence hot during Shabbos.

Pouring the essence into a k'li sheini heats the essence, is that not bishul?

It is not bishul because the essence was cooked before Shabbos and the Mishna Berura writes that one may reheat cooked liquids in a k'li sheini. [7]

If one forgot to prepare tea essence before Shabbos, how is one to drink tea on Shabbos?

           1. Borrow from a neighbor.

2. According to the poskim who hold that ein bishul bik’li sh’lishi, [8] one may put the teabags into a k’li sh’lishi. I.e. pour water from the urn into a cup, pour it into another cup and then put the teabag into the water.

3. However, many poskim are of the opinion that items that cook easily may not be placed even into a k’li sh’lishi or any other k’li that is yad soledes bo. Accordingly he will have to forgo a hot cup of tea that Shabbos.

Summary: 1&3 are preferred, 2 only if your Rav paskens so.

Is it permitted to pour hot water into a thermos on Shabbos?

The issue involved is hatmana – storing food in wrappers to maintain heat. As we have previously learned, it is forbidden to totally enwrap a hot food on Shabbos with intention to maintain its heat. However, there are two reasons why it is permitted to pour water into a thermos: 1) hatmana is forbidden only when applied to the original pot, but if the water has been transferred to a second pot, it is permitted. [9] 2) Hatmana must be done to a pot but the pot itself is not hatmana, and since the thermos is considered as one pot with a few linings it is not hatmana. [10]

The fire under my blech went out, and I would like to enwrap my pots within my bed linen, may I?

No you may not because hatmana – enwrapping, when done on Shabbos, is forbidden even when there is no heat source present. You may however, partially enwrap the pots. [11] The same applies when you realize that the socket of the hotplate is out and you want to preserve heat. One may partially wrap the hot pots but not enwrap them entirely.

 Am I permitted to warm my baby’s bottle by placing it inside a pot of hot water?

Several poskim agree that it is not permitted to immerse the entire bottle into hot water in order to warm the bottle for the same reason as in the previous answer. You may however, insert the bottle leaving the top uncovered. [12] The logic behind that is that hatmana means to entirely enwrap a container to preserve heat. Leaving a noticeable portion of the container uncovered does not constitute hatmana.