Do these rules tell you the remainder, or only yes/no?

The digit-based rules actually give the remainder, not just divisibility — the test value is congruent to the number.

The digit sum equals the number mod 9 (and mod 3); the alternating sum equals it mod 11; the last-two-digits equal it mod 4. So they double as quick remainder finders:

• 1,238 mod 9 = digit sum 14 → 5. (Indeed 1238 = 137·9 + 5.) ✓

"Divisible" is just the special case where that remainder is 0. This is exactly why casting out nines (next mission) can check arithmetic — the same congruence underlies both.