Learn English – “Is it okay for you?” Is this phrase considered formal in school/college setting

The phrase and all that is strictly informal, because it’s sloppy.

A person says and all that when they know that greater precision is called for but they don’t want to make the effort to find words to describe the category they’re talking about. It’s common and ordinary in everyday, informal speech.

It’s grammatically correct even without a word after that. That functions as a demonstrative pronoun, and all modifies it to mean that you’re regarding that as a whole somewhat carelessly, without regard to details and distinctions.

An informal phrase in a formal context

One reason you find and all that in books is because it occurs in dialogue. Books are normally written in formal English, but they can contain informal English in quotations. In indirect speech, appending and all that can suggest that someone is taking a sloppy, dismissive attitude toward a topic. (In informal contexts, the phrase doesn’t carry the connotation of dismissiveness nearly as often.)

Occasionally, deliberate informality in a formal context makes good rhetoric. For example, there is a textbook on vector calculus titled Div, Grad, Curl, and All That. The title, by using the phrase and all that, suggests that the book will cover the topic informally, in a tone and style that are easier to understand than the very formal approaches more commonly found in math textbooks.

The phrase and all that occasionally appears in book titles or other formal contexts to allude to a parody of English history, 1066 and All That by Sellar and Yeatman, published in 1930. Its premise is that it presents English history as you actually remember it from school. For humor, it mixes things up and reduces people and events to absurd simplicity. For example, the book incorrectly calls Alfred the Great “Alfred the Cake” because of a famous story about the real Alfred and some cakes. It rates nearly every king “a good king” or “a bad king”. The book is well-known enough that people sometimes write and all that to designate an irreverent or false history of another topic, either a deliberate one or the way people have misremembered it.

Formal equivalents

There are equivalent phrases in formal English that also avoid explicitly describing some category, leaving the reader to fill in the details: and the like, and such, and similar things. If you can replace things with a more-precise noun, that’s better in formal English. Another formal choice is et cetera, Latin for “and the rest”, usually abbreviated etc.

You could do a lot with this item, such as writing, drawing, and the like.

You can do a lot with this item, including writing, drawing, and the like.

With this item, you can do writing, drawing, and the like.

I removed your first like to avoid repeating the word.

In this particular example, it’s probably better to avoid the phrase entirely, since like, such as, and including all clearly indicate that the list is not exhaustive:

You can do a lot with this item, including writing and drawing.

That has the clarity and crispness of formal English.

In the Cambridge Encyclopedia of the English Language (2003), thanks is considered a minor sentence, or more specifically, a type of minor sentence that is a "formula for stereotyped social situations."

In chapter 8 of "An Advanced English Grammar with Exercises" (1913):

Good usage does not demand that all sentences shall be absolutely complete. It often allows (and sometimes requires) the omission of words that, though necessary to the construction, are so easily supplied by the mind that it would be mere waste of time to utter them.

The first example of such an elliptical sentence is:

[I] thank you.

"Thank you" without an explicit subject has been used since at least the 15th century, according to an article in the ICAME Journal (vol. 26:63–80):

Interestingly, the shift from a clearly performative speech act with a subject, e.g. I thank you or I give thanks to you to the shortened forms thank you and thanks, had not gone far in Early Modern English. The shortened forms appeared in the 15th century and there are only five examples in my material [Corpus of English Dialogues].

So, although it is generally regarded as grammatically correct, it might sound too informal for business communications. That is entirely subjective, though. Of the alternatives you provided, I think the one beginning with "we" sounds best (see edit below):

We thank you for the information...

Alternatives to thank you can also give the letter a more professional tone:

We appreciate the information...

We are [very] appreciative of the information...

Our company is [very] grateful for the information...

Edit:
Rather than rely on my own assumptions, I tried to find more references for business writing etiquette with regard to thank-you letters or letters of appreciation. I think now that my opinion was wrong about the implied subject for thank you being too informal for business communications.

I found a reference from the American Management Association, The AMA Handbook of Business Writing (2010), which gives examples of several types of business letters. In it, there is an 8:3 ratio in favor of using the implied subject form, "Thank you," rather than for example, "I want to personally thank you..."

In another book with business letter examples, 300+ Successful Business Letters for All Occasions, the first example of a Thank-you letter (pg 51), begins with "Thank you..." The second example on page 52 also starts with the implied subject form, although the last sentence uses an explicit subject "We thank you..." The examples of other types of letters often use of the implied subject form, too.