The question is motivated by the Israel-Palestine conflict, but it may be asked/answered in general. I am wondering if Geneva conventions or any other international regulation forbid a country (Israel in this case) to attack or kill civilians and especially children if the other part uses them as human shields.
No, it does not forbid it.
The Geneva Convention establish the standards of international law for the humanitarian treatment of war
Geneva Convention IV Article 28 of the 1949 Geneva Convention IV provides: “The presence of a protected person may not be used to render certain points or areas immune from military operations.”
The loss of civilian life must be proportional to the military advantage gained.
Additional Protocol I Article 51(5)(b) of the 1977 Additional Protocol I prohibits an attack which may be expected to cause incidental loss of civilian life, injury to civilians, damage to civilian objects, or a combination thereof, which would be excessive in relation to the concrete and direct military advantage anticipated.
Subjecting civilians to military attacks by using them as human shields would make Hamas guilty of war crimes.
With respect to non-international armed conflicts, Additional Protocol II does not explicitly mention the use of human shields, but such practice would be prohibited by the requirement that “the civilian population and individual civilians shall enjoy general protection against the dangers arising from military operations”. It is significant, furthermore, that the use of human shields has often been equated with the taking of hostages, which is prohibited by Additional Protocol II, and by customary international law (see Rule 96). In addition, deliberately using civilians to shield military operations is contrary to the principle of distinction and violates the obligation to take feasible precautions to separate civilians and military objectives (see Rules 23–24).
The Customary international law is made up of rules that come from "a general practice accepted as law" and that exist independent of treaty law. Customary international humanitarian law (IHL) is of crucial importance in today’s armed conflicts because it fills gaps left by treaty law in both international and non-international conflicts and so strengthens the protection offered to victims. The 161 rules of customary international humanitarian law worked out by the ICRC gives a very clear answer: NO.
Rule 89 mentions that “Murder is prohibited”. You can read the whole Rule in this web address: http://www.icrc.org/customary-ihl/eng/docs/v1_cha_chapter32_rule89
Children are hors de combat, since the Protocol I to the Geneva Conventions defines it as a person is 'hors de combat' if:
(a) he is in the power of an adverse Party; (b) he clearly expresses an intention to surrender; or (c) he has been rendered unconscious or is otherwise incapacitated by wounds or sickness, and therefore is incapable of defending himself; provided that in any of these cases he abstains from any hostile act and does not attempt to escape.
However, in this case, children are children and they are in their own houses.