(...) capturing groups: numbering and what comes back

Numbering follows the opening parenthesis, which makes nested groups easy to read once you know the rule: the outer group is always numbered before the inner one. Matching /((a)(b))/ against "ab" gives four entries, the whole match, then the outer group holding ab, then a and b. Counting closing parentheses instead is the usual source of an off by one.

A group that did not take part is undefined rather than an empty string. In /(a)|(b)/ exactly one branch matches, so the other group's slot holds undefined, and code that calls a string method on it throws. That is a real distinction: an empty string means the group matched nothing, while undefined means the group was never reached.

Quantifying a capturing group repeats the match but not the capture. /(\d){3}/ matches three digits and leaves only the last one in group one, because each iteration overwrites the previous value. When the whole run is what you want, the quantifier belongs inside the parentheses, as in /(\d{3})/.

Capturing has a cost in both directions. It makes the engine record positions it might not need, and it fixes the numbering of everything after it, so inserting a group in the middle of a pattern renumbers every later reference and every $1 in a replacement string. Anything grouped purely to apply a quantifier should be non capturing.