Question

Когда законопроект становится законом?

Answer 1

Ответ на него абсолютно однозначен – законопроект становится законом после третьего чтения (принятие законопроекта в целом). 
Т.е. еще до подписания председателем ВР, до подписания Президентом и уж тем более до опубликования. 
Зачем было все это городить - не понятно. 
Что означает фраза " опублікування та набуття ним чинності, тобто, власне, того моменту, коли законопроект стає законом.", также непонятно.

Answer 2

When Does a Bill Become a Law?

In general, the process of a bill becoming a law involves several stages and varies by country. In the United States, for example, the process involves the following steps:

Introduction of the Bill: A bill is introduced in either the House of Representatives or the Senate.

Committee Review: The bill is reviewed by a committee, which may hold hearings, amend the bill, and vote on whether to send it to the full chamber for consideration.

Debate and Vote: The bill is debated on the floor of the chamber, and members may propose amendments. After the debate, a vote is taken.

Conference Committee (if necessary): If the House and Senate versions of the bill are different, a conference committee may be appointed to reconcile the differences.

Presidential Action: If the bill is passed by both the House and the Senate, it is sent to the President. The President can either sign the bill into law or veto it. If the President vetoes the bill, Congress can override the veto with a two-thirds majority vote in both chambers.

Becoming Law: If the President signs the bill or if Congress overrides a veto, the bill becomes law.

Citations: - Source "A bill is introduced in either the House of Representatives or the Senate." - Source "The bill is reviewed by a committee, which may hold hearings, amend the bill, and vote on whether to send it to the full chamber for consideration." - Source "The bill is debated on the floor of the chamber, and members may propose amendments. After the debate, a vote is taken." - Source "If the bill is passed by both the House and the Senate, it is sent to the President. The President can either sign the bill into law or veto it." - Source "If the President signs the bill or if Congress overrides a veto, the bill becomes law."

In other countries, the process may differ, but generally involves similar stages of review, debate, and approval by the relevant legislative bodies before it can become law.