Legendaries missing?

So while I was stuck in the progression of the story(in cinnebar island), I decided to hunt for some legendaries and other pokemon while waiting for a fix. I caught a mew in the pokemon mansion(random encounter) and I was really happy. But now I went hunting for the legendary ice bird, Articuno. I did manage to go to the islands and the spot where Articuno is supposed to be but no one was there.
Just look at this empty spot where Articuno is supposed to be(I have neither met, battled or captured Articuno):

Maybe there is a bug where the legendaries don't appear on the map like they should! Please look into this issue as well.

Zapdos also missing, found Zaptos as a random encounter though.

location of random encounter:

empty real location:

First of all, It's not a bug or error. You can't see the legendary birds npc because of the event "the power of one".

The legendary birds npc's, only appears when you have lugia in your party.

And another thing, all legendary pokemon until hoenn, they will be in wild encounters and they have 5% only.

Note that legendary pokemon is like a "bonus" in my game in this way.

I put Mew in the pokemon mansion because of the event "mewtwo strikes back" and because it's an old secret lab long time ago.

My game is not a 100% remake from the original games, i changed a few things to turn the game more challenging.

OK. Thanks for clearing that up. One question though, can I then catch multiple Mew for example or is it only 5% until I have captured it and what if the legendary Pokemon would accidentally faint?

Like i said before, only basic pokémon forms until hoenn region are wild, and it will be unlimited on wild, same for legendary, except for babies pokémon like pichu for example.

The game remakes the older games to generation 3 games (fire red / emerald example) and then i make that few alterations.

So in this game you can have for example: 4 Mew or 7 articuno and so one.

But the game offers 720 oficial Pokémon, but pokemon from sinnoh, unova and kalos will be consider as bonus in a mansion on celadon city as prizes.