Rotting plants can cause ammonia. But live plants are much better for an aquarium than fake plants. I could never get live plants to grow till I discovered that the kind that grow attached to decor worked for me - I have Java fern, several species of anubias, bolbitis and several species of bucephalandra all attached to wood. And I have water sprite as a floating plants.
There are a few ways to cycle a tank.
By adding ammonia to the tank and following the method in the stickies of the Cycling forum. Bottled bacteria can be used to speed the cycle, eg Tetra Safe Start.
With live plants - though the plants need to be healthy and actively growing, and more than just the odd one or two.
Using fish as the source of ammonia to do a fish-in cycle.
The first two should not have ammonia in the tank after fish are put in. Fish-in cycling does mean ammonia, and nitrite, in the water but even a fish-in cycle should have completed by now.
How high is the ammonia in your tank?
There are a few things you can do.
Water changes to get the ammonia down to the level in your tap water.
Get some Tetra Safe Start
Buy some floating plants. These take up ammonia faster than plants lower down in the tank because they can get their carbon dioxide from the air. You can use fake plants as well, but floating live plants are a good thing to have in a tank. Anything from Salvinia, though water lettuce and Amazon frogbit to water sprite - and hornwort and elodea/egeria/anacharis (same plant, different names) can be used as a floating plant.
I would ignore the pH for now, concentrate on the ammonia. And nitrite if you get a reading above zero for that as well..