Yes, and I put them both on the same page (just need to correct the jlpt markers on this page).

Thanks - fixed that up, and went ahead and added a few more model sentences to help out :)

For some reason, in the first usage, second example sentence, there is 住みません for 済みません・すみません. Otherwise, should that か which follows not be が？

Ah right, sure

Yes, you can use しかない as per your example sentence. As for the だ: ない here is just ありません or the negative form of the verb you're using so the same rules apply as when you're using the negative form in other sentence constructs. Did that answer your question? :o

Should not be there, removing it now!

Updated!

it is the polite form of the negative. For 書く, you've got 書かない (short negative) 書きません (polite negative) The でした is the past tense. Teeeeechincally, only the first is the 'ない' form, but it would take up too much space to add every negative form. Maybe ..use 'Negative form' in the box in the future.

It's hard to say without seeing the full sentence, but I imagine it was something like the following from the site's library: 私は、１０冊しか本を持っていない。 (I have no more than ten books)
If that's the case, this falls under the first usage.

It's easier to understand if you think of しか as describing the action/verb.
For instance in 一枚しか作文を書きませんでした (I've only written one page of the essay) from above, "one page" describes how much I've written, not the essay itself, so 一枚しかの作文 would be wrong.
Likewise, in 彼しか事実を知らない (only he knows the truth), "he" describes who knows and not some aspect of the truth, so 彼しかの事実 would also be wrong.
I hope this somewhat helped clear up the confusion.

I wouldn't say it's quite similar to だけ. The way I think of them is that だけ means "only", without any suggestion that it is a smaller than expected/normal amount.

You are right in that only that option exists, so one is "stuck to it" - but this only applies to しか.

Fixed, thanks!