Hi,
The time it takes for the ammonia to drop is very variable. It depends on so many factors - the temperature, the pH, the hardness, and how many bacteria manage to survive being poisoned by the water company - they add chlorine or chloramine to disinfect tap water and it also kills our filter bacteria. When I did a fishless cycle last year, I counted the day I added the first dose of ammonia as day 1, and I saw a drop on day 13. Yours could be quicker than that or slower, but that timing seems reasonably typical. And it was day 32 before I saw a drop in nitrite.
But I was using a modified version of the old fishless cycle method, starting with just 1ppm ammonia, then adding the same dose every time ammonia dropped to zero. The current thinking is that it is not necessary to add more ammonia as soon as it drops to zero. If I'd known about that method when I did a cycle, I would have tried that instead.
Contrary to what I used to believe, it seems that having plants in during cycling is not a thing to avoid. The only 'problem' you might encounter is more algae than if you didn't have live plants, simply because without plants you can leave the lights off.
Siamese fighting fish vary quite a lot in temperament. Some are very laid back and easily bullied; some will attack anything that moves. And everything in between. Endlers are reputed to be OK with fighters (no long flowing fins, and they tend to keep any nippiness among themselves). Platies - maybe. They are quite brightly coloured and if you have a particularly aggressive fighter he could mistake a platy for another fighter. The one I'd be concerned about is the rainbows. Males have quite long threadlike fins, which could trigger a fighter's attack instincts.
What I'd do is get the fighter last so he'll be going into an environment that already has fish. If you get him first, he'll see any later additions as invaders of his territory.
And have a back-up plan just in case. A short term measure, should things go wrong, is one of those fry nets that clip on the side of the tank for the fighter, though as fighters can jump you would need a cover. This would give you breathing space to decide what to do. If your fighter does get picked on or won't tolerate tank mates, long term you would have to rehome him or get another tank just for him. 20 to 25 litres is fine for just one fighting fish - this is how multiple tank syndrome starts

Multiple tank syndrome - an incurable condition that affects fish keepers, characterised by the desire to have more and more tanks.