OK, overfeed the tank where the new filter is. Fish food breaks down whether the fish eat it or bacteria eat it, and becomes ammonia that feeds the bacteria.
Yes, a heavily planted tank will be all the bio filter you need, as long as the plants are healthy and thriving. The plants will bring in some bacteria on their leaves, too.
Some substrates are pretty high in fertilizers to get your plants started, but over time the plants use those fertilizers, so you will need to add more. Dry ferts are more cost effective than buying bottles of water with just a little fertilizer in them.
GH and KH measure different things, so it is entirely possible to adjust each separately.
The KH is related to pH, so there is a link there. In general when you raise the KH the pH will also rise. When you dilute your tap water with RO, so the KH goes down the pH is more liable to vary. Something else in the tank is dictating the pH.