An attempt to clarify the capture rule for beginners.
During Black's move, after Black has placed a stone, Black may remove any stones of White's that have 0 liberties. Then Black (White often assists) removes any Black stones that have 0 liberties.
It is important that these two stone removal activities are distinct. See RulesOfGoIntroductory#example4
Many rulesets consider it an illegal move to place a stone that is removed during the second stone removal activity (before any other stones have been placed.)
Beginners often play moves that capture themselves, or other stones, without the player(s) noticing and play moves on. When a more experienced player is their opponent, that player usually brings attention to such oversights.
The following avoids the need for such interventions.
During Black's move, before Black has placed a stone, Black may remove any stones of White's that have 0 liberties. (Should one be found, the previous move is considered a pass.) Then Black places a stone and again, removes any White stones that have 0 liberties.
For example
Thank you for your comments, which I have used to try to improve the section on capture so as to avoid misunderstandings.
One problem is that we do not want this particular page to get any bigger than it needs to be: it is meant to be the bare minimum required to get people off to an easy start!
I think you are right that there is this possibility for confusion which some people feel, but I also think that different people stumble over different things, and if we deal with them all at any length the page will get bloated. Of course the rules must be clearly and correctly stated, but I think it is fair to expect people to re-read them if in doubt, and I think that if they do, they will find the answer to this problem.
As you have evidently know, rules on suicide vary, but here we just want to present the simplest version to get people started. As for regulations for how to cope when people do make mistakes or rules to compensate, that also goes too far for this page. But I shall leave it to others to analyse your suggestions in more detail, or suggest where one might describe these ideas on the site.
[RulesOfGoIntroductory#example4]
WX