I'm going to thread very lightly saying this, as I don't want to provide misinformation. This is all to the best of my knowledge.
For Gen 6/7, it appears the PID and other values that were associated back in Gen 3/4 can be modified freely,
because I was told "the RNG system is sufficiently random". However, with the correct seed, those values could be predicted (hence allowing for RNG to even work).
If you look at the screenshots in this page, you'll see that there's a program that accurately predicted PID, Ability, Gender, IVs.
(I've managed to obtain the shiny Hat Pikachu based on that program's work + the NTR overlay)
With that being said, it might take an impossible amount of computing power to reverse RNG search based on PID and stats.
Since I'm not a developer nor do I thoroughly know how the 3DS RNG system works, I can't guarantee it is not impossible in the future.
Now that I've laid down the context, here's to me answering you part-by-part.
Yes, while coded differently, people have been able to RNG pokemon accurately in those games.
Refer back to my statement regarding "I can't guarantee it is not impossible in the future"
Refer back to my statement regarding "I can't guarantee it is not impossible in the future"
Frankly, I got no clue regarding this. I need to read up on whether TID/SID RNG can be done in Gen 6 and 7.
Even in Gen 3 and 4, they weren't always generated as pairs at the start of the game, so can't say definitively.
Trainer Name shouldn't be a problem. As for TID/SID, read the block directly above this response (I can't definitely say portion)
Closing Statement
Ultimately, if we look back at an earlier reply I made to you:
I cannot give you the 100% guarantee you appear to be seeking. If you want to hack, you need to accept some risk on some level.
Granted, I think it is good that you want to know what can and cannot be done. It beats being a noob that just makes fake hacks and screwing themselves over.
It is probably safe to do as many edits as you want to do presently, but who knows if the system is going to change in the future?
The next best advice I can offer you, if you still have doubts, is to:
1. refrain from hacking entirely or
2. Perform limited/small edits, but keep a note somewhere of what edits you made. IF anyone (else) gets banned somewhere down the road, we'll likely report it.
We may (or may not) find out how these bans came to place, and you could check whether you've made that offense.
Tho of course, I also cannot guarantee what led people to be discovered.
[edit: For the record, I myself no longer directly modify my games that I use for online services, even if I don't battle others.
If I need to make edits, I'll modify the Pokemon on another game on another 3DS, then trade it over to my main game.
So the advice I'm giving you isn't something I'm just preaching without practicing ]
There was a time that certain people appeared to have gotten banned from Game Sync/Global Link (myself included).
As for me, it was something as easy as changing my 3DS save region when it's impossible.
For others, it appears to have been having one hacked Arcanine (invalid form ID) or perhaps impossible amount of balls in the Bag.
(I could find you that link if you want. Keyword was probably Banhammer Strikes again or something)