According to this page on the etymology of the word 「切ない」, the 「ない」 in it is not the 「ない」 that means "there is no ...", but rather an ending that turns the noun 「切」 into an adjective.
On the other hand, there are many adjectives ending with 「ない」 that does seem to mean "there is no...", e.g. 「そっけない」、「あどけない」.
Is there any connection between the 「ない」 in 「切ない」 and the 「ない」 that means "there is no ..."?
If the answer to 1 is no, are there a whole series of adjectives ending with 「ない」 that acts as an adjective ending? If so, what are the most commonly used among them? How about such words as 「すくない」, 「きたない」, etc.?