The point of working with these note numbers [scale degrees] is the sound of them, or really, the relative sound of them.
In the last tune, where is the tonic, note 1? What key is the tune in? Well, it does not really matter for writing down the tune.
What we need to decide upon is the tonic. Where is note 1? We can decide that without knowing which actual note name it is. Note 1, the tonic, is the note which the tune is 'leading' to, the note which makes the tune sound finished, the note we would sing at the end of the tune.
The tonic is the first note of the scale of the piece. Hum some songs to yourself. There is a note in the song which sounds like the end of the tune [or the beginning too], the tune 'wants' to finish there, it sounds like the natural finishing note. This is the tonic.
It is also note 1 of the scale of the tune. Which scale? It does not matter. We have note 1, so now we have all the notes of the scale of the piece because they are all relative to the note 1.
So now we can write down the note numbers of the tune, by deciding on the note 1 and how each note relates, fits in with, this note 1.
But what notes are we hearing? It does not matter. But let's call the note 1, C. Now we are using the C scale and we can write the tune down using C scale. If we call the note 1, say, G, we can write the tune down in G, using the G scale.
Now this will not worry us unless we have a very strong sense of what the notes actual names are.
If we want to know the actual key of the tune we decide on the tonic, as we have been doing, but now we need to test this note against other notes.
At first, it might be best to use a guitar or keyboard. Hear the tonic of the piece, find it on the guitar or keyboard. We repeat this until we find the note. We get better and faster at this with practice.
Now, we don't just 'know' the note name of a note that we hear. Most of us need to relate that note to notes on an instrument, a guitar, keyboard or harmonica, for example. Other instruments are not so helpful because many of them sound different notes to what the player would call them, they are transposing instruments.
Anyway, having decided on the tonic of a tune we find it on an instrument and now we have the key of the tune. ----------
Joe, may I make a suggestion? I don't know if you've clicked on my 'Thread Organizer' link, but you might do something similar in your signature. Basically, you pick one of your threads to serve as a base page and bookmark it in your browser, and when you add a new thread with new info, you make sure to put a link to it in your master thread. Then, all anyone needs to do to find all your threads is click on your link. It's the closest thing we have around here to being able to make channels and it might make it easier for people to read your stuff sequentially, since the search isn't always helpful. :)