When speaking about oneself 私{わたし} is always OK for both genders for any age. For boys (and some tomboys) 僕{ぼく} is also used. You may also hear あたし which is used by slightly older females (High School age onwards) in casual situations.
A: If you know their name then their name. Else あなた or 君 or 私/僕(if they have already referred to themselves as such).
B: If you know their name then their name. Else お兄さん・お姉さんor あなた or 君 or 私/僕(if they have already referred to themselves as such).
In the case they have both referred to themselves as 私・僕 and you want to refer to them both as the same, then facing said person and/or addressing them(body movement-wise) would allow you to use私・僕 in most cases. Otherwise referring to the younger as私・僕 and the older as お兄さん・お姉さん would, in most cases, be ok.
C: If you know their name then their name. Else お兄さん・お姉さん。
D: If you know their name then their name. Else 弟・妹(with optional あなた・君の___)。
Alternately in all cases, asking their names really wouldn’t hurt.
Situation 1
Running on from the explanation above (A-D), depending on what has been established in the conversation, would determine what each child would be called. If the speaker knows neither, and neither has addressed themselves yet, then あなた or 君 would be fine (in most instances). Further, following A and B (above) would follow the usage. As to who gets priority when the word 僕 is used, that depends on who is older/who refers to themselves as such/who you are focussing on. Take the example of talking to two Peters, when you address the one on the left, you do not say “Peter on the left”, you would focus on said Peter and address him as “Peter”. The Peter on the right would notice the attention is not on him (assuming he is paying attention) and thus would assume you are intending to talk to the Peter on the left. There are situations when the speaker would refer to the elder one as 僕・私のお兄さん・お姉さん, mainly where the younger one has established that they are 僕・私 and you ask a question to the younger one pertaining to the elder one.
The most natural (and clearly most understood) way of referring to each would, in almost every instance, be by name.
Situation 2
This question is difficult as we do not know the context of each child’s relationship to each other. If the children are school friends you may here the younger child referring to the older one as 先輩 and the older one refer to the younger one by name. If however, they are rather close (best friends, neighbourhood friends, family friends), it would not be uncommon to hear them call each other by name.
2.1
私 is always ok in any context (even business although you will most often hear 私{わたくし}) to use to refer to yourself. 僕 is ok in most situations but is not acceptable in most business situations (a problem you shouldn’t face talking to kids). Depending on your age in regards to the children, you may also refer to yourself as お兄ちゃん・お姉ちゃん or おじさん・おばさん or even お爺{じい}さん・お婆{ばあ}さん. This runs off of the question you refer to in your post in that if you refer to a child as 僕 or 私 the way to identify yourself within the conversation becomes an age statement comparable to your child audience.
2.2
The age range to use お兄さん・お姉さん when related to a person can be an order of minutes (in the case of twins etc. one is usually the older twin). When referring to yourself as お兄さん・お姉さん age wise you are usually High School Age to 30yo. This is not a set age and usually can be ascertained by what the child refers to you as. Similarly self-reference terms do not become obsolete as changing the terms to fit your age accordingly (お兄さん＞おじさん＞お爺さん).
2.3
This is highly contextual as to how so far you have been referring to the children in your conversation. If you have referred to younger sibling as 僕 and the older one as お姉ちゃん, then use of お姉さん to refer to yourself would be understood, however this would be more noted by vocal inflections and pronunciation. Using or not using the お is another way in which you can break up the references. Referring to the older sibling as 姉ちゃん and yourself as お姉さん would make the references noticeably separate.
※ It is also of note that the age of the child and vocabulary will reflect how much of the references and context they can understand. It is also of note that like any relationship in any language anywhere in the world, people refer to each other how they feel comfortable referring to each other. Children are no different. I have listed common usages however, this is an definitely a non-exhaustive list.
Once again, the most natural (and clearly most understood) way of referring to each would, in almost every instance, be by name.
