The fact that John begins with the children is because that's where a believer begins his walk (relationship)--vs.12 "because your sins are forgiven you for his name's sake"; and as a new born babe what is imperative is that a believer understand that he has been received into the family God (Gal. 4:4-8) and now is considered a "son" and now know God as Father--vs.13 "because ye have known the Father". Regarding the order of fathers first, then young men second and children last in verses 13+14, I would say It is in order of authority in the body of Christ. The elders having more experience and having their senses exercised to discern between good and evil,they know (understand) "Him (God) that is from the beginning" and have a charge to look out for the younger (1 Pet.5:1-5, Heb. 13:17). And the younger have a charge to submit themselves unto the elder (1Tim. 5:1, Heb.13:17, 1Pet.5:5). As you have noted the message to the fathers in verses 13+14 is the same, "ye have known him that is from the beginning" And the message to the young men is essentially the same "ye have overcome the wicked one"; the difference in verse 14 is John shows how the young men overcame, "men, because ye are strong, and the word of God abideth in you". As is common often the same thing is stated twice to bring emphasis to the statement. But where we seem to see things differently is in your statement:
"So, my main question here is this: Why John chose exactly these unique things for each one of the three groups (in other words, why is it specifically about sins when it comes to children, why is it specifically about the wicked one when it comes to the young men, and why is there nothing negative at all, when it comes to fathers)?"
I can only see positive things being addressed to the children: vs.12 "your sins are forgiven you for his name's sake" and vs.13 "ye have known the Father". And only positive to the young men: vs.13 "ye have overcome the wicked one" and vs.14 "ye are strong, and the word of God abideth in you, and ye have overcome the wicked one". It seems like your question is more of a statement than an inquiry. As though there is some hidden deeper meaning in looking for negatives in the address to the children and young men (where none is stated). For me, the children are introduced into the kingdom and realize their sins are forgiven. The young men continue in the way and come to realize that they are in a spiritual warfare and learn to overcome the enemy through their knowledge of the Word and trust in the grace of God. The fathers are settled (1Pet.5:10) into the way and help the younger to attain unto "the stature of the fulness of Christ" (Eph.4:11-14).