Learn English – When would you vs when you would in a sentence

The second sentence has no literal (or idiomatic) meaning at all; it simply does not parse correctly.

The first sentence means "The purpose of this [letter or whatever] is to make sure you're informed that we have carefully reviewed your estimate on the parking lot refurbishing."

If you want to get tricky, you can rearrange things a bit to say "This is to you inform that…", but this is archaic and confusing even to most native speakers. Don't try it unless you're writing poetry. (It's basically identical in meaning, just switching around the verb and the object. The only difference, besides being pretty hard to understand and having a different rhyme and meter, is that it emphasizes the object a little more. Think of it like "to inform you", except subtler.)

The rule you are referring to ("no will" with when) only applies in those sentences in which when introduces a time clause, e.g.:

*Give me a call when you will get my message.

Give me a call when you get my message.

In your example, when introduces a sort of reported speech, it is not a time clause. It is as if it were derived from direct speech along the lines of:

"When will he be back?" - "I don't know"

Therefore, it is correct to join the two sentences as:

I don't know when he will be back.