1. That's the preferred method, which makes it easier to read, but you can use sentencecase and punctuation.
2. I err on the side of formality and write Dear Mr. [LAST NAME].
3. Any kind of paper is fine so long as it's legible.

Hey there! :-)
I want to send a letter from Germany to the US and I have a few questions...

1. Is it correct that the address on the envelopes must be written in capital letters and that no punctuation is allowed?
2. How do you start your letter? I want to write to an actor who is just a couple of years older than I am (he's in his early thirties). Is it okay to start like this: “Dear FIRST NAME?“
3. What kind of paper do you use?

Thanks in advance! :-)