Is the opposite of 'within', 'without'?

No, we cannot use without as opposite of within or as holding a meaning 'outside the bounds of'. It can't be used for that purpose.

They are not antonyms of each other.

Without is the (negative) antonym of with, and that's the end of that story.

Within means inside, and the (opposite) antonym would be outside. (This fits "the bounds of the law" or "the warranty period.")

EDIT: Others have suggested that your proposed usage, while archaic, is still correct. Beware the distinction of negative vs. opposite:

• "Without the bounds of the law" would imply that the law was not bounding him, or inapplicable, not that he was dodging it.

• "Without the warranty period" would imply that there was never any warranty, not that it had lapsed.

The usage you suggest does not exist in modern English. It is incorrect in your examples.

It appears that it can also be used in that sense, though less common.

without

• On the outside: a sturdy structure within and without.

The Online Etymology Dictionary has reference to your issue.

without (adv., prep.) Old English wiðutan "outside of, from outside," literally "against the outside" (opposite of within), see with + out (adv.). As a word expressing lack or want of something (opposite of with), attested from c.1200. In use by late 14c. as a conjunction, short for without that.

within (adv., prep.) Old English wiðinnan "within, from within", literally "against the inside", see with + in.

There is a hymn that starts with the words, "There is a green hill far away, Without a city wall." Here the word without clearly means the opposite of within. It is archaic but it certainly used to be used in this sense.

Yes, without can mean lacking / absence of OR outside.

Without is a broader term, covering both lacking and the absence of, and also means outside. (This double meaning led to the Marx Brothers routine: There's a girl waiting without. Without what? Without food or clothing. Well, feed her and send her in.)

Source. Safire, William. A version of this article appears in print on March 28, 1982, Section 6, Page 10 of the (NYT) National edition with the headline: The Present Absent On Language.

In Scottish English (not dialect or Lowland Scots) the term is:

Outwith

Which as an Englishman I had never encountered until I moved to Glasgow, where I found it used in academic circles.

You will find it in Chambers Dictionary (not online but on the iPhone app) where it is defined as:

preposition (Scot) outside of

adverb outwards