Is it correct to write "You" with a capital Y as a form of politeness? If yes, should I use that form throughout the entire letter/document, or only at specific places?
No, it would be seen as unusual, perhaps archaic. The only reason I is capitalised is that i doesn't stand out visually, and needs added visual emphasis. He, Him, and His are capitalised when referring to God (or variations thereof) in Jewish, Christian, and Islamic texts. In that context, You and Your (or more typically Thou, Thee, Thy, and Thine) would also be capitalised.
Certain titles such as Her Majesty the Queen also include capitalised pronouns, but simply because they're titles, like Doctor or Professor.
Ditto Jon Purdy that we do not normally capitalize "You" in English. I can think of only two exceptions. One is the case already mentioned, references to God. The other is some legal contracts that have a section of definitions at the top where they carefully define "You" or "YOU" to refer to a specific category of person, like, "By 'You' we mean a person who has registered as a client of our company, who meets the requirements detailed in section 2.3.B, and whose membership is fully paid as of the date ..." etc etc. Then in the text they put "You" or "YOU" instead of a plain "you" to remind the reader that they are using the word in this very specific sense.
I definitely would not capitalize "you" just to show politeness or respect. Few English-speakers would understand that that was your intent. They'd just wonder why you used the odd capitalization.
I think it is not weird to use capital Y in 'You' because unlike in French and Hindi where You has the form "vous" and "aap/tum" respectively, to show more respect and politeness, English lacks it completely. In that sense it is not weird at all.
However, it is true that it might strike some people and that it is used in English referring to God. But i read a fantastic article some years back that convinced me to write a small "i" instead of a capital one, and to make the y capital in "You" to show more respect to the person, and attach a modesty to oneself.