1. How do you do? - I might still use it, rarely. For example, if I was being introduced to a grande dame relative of yours in a fancy French restaurant, or to someone at the ambassador's residence.
2. Howdy - I use this all the time, though I didn't always. I have a feeling it started (with me) as a contraction of 'How ya doin' which in turn is a contraction of 'How are you doing'. (I am not a cowboy, nor from the South. I can moo, if it's late, and given enough to drink.)
3. Never heard 'all right' as a question, and can't even really imagine it that way. (As a separate issue, it's two words here, and not 'alright'.) I use it as a response to 'How are you', but pronounce it 'awright'.
4. I'm fine / Angenehm - quite analogous. Frankli et al: By no means is there anything wrong with answering how you really are in English. 'So-so', 'Fantastic! I just got a raise!', 'tired', 'still hung over from last night, but recovering' are all possibilities. Naturally, you would still say 'Fine' to those you didn't know well. And you would normally lie about truly grave situations, so that if you were suffering extreme pain from bone marrow replacement and radiation therapy, you would either say 'Fine', or 'so-so', but not 'I'm in extreme pain and expected to die in a few weeks or so'. But I expect the same is true in German.
5. Gambit: Rodo, I try to write here the way I normally would to monolinguals, knowing that sometimes this might cause some puzzlement, but thinking that this is also a way to learn. I hope this is okay. I prefer that German speakers also use the full range of their vocabulary, as well. I do occasionally run into problems when they use slang or dialect, and also when they use combined forms which are frequently not in Leo or other dictionaries (why not?) but usually I can figure them out, if I can decide where to break them and look up the parts.