Will Partial WC Increase KH?

What is your nitrite reading now? You say nitrites appeared but not if they have now disappeared. The cycle is finished when both ammonia and nitrite stay at zero without having to do water changes.
Nitrate tests are not terribly accurate and are best used to monitor a trend, like a continual rise to show the last stages of cycling. Yours is going up which shows you are near if not actually at the end. Nitrate will increase as the nitrite eaters grow, but the cycle is only finished when you have enough to eat all the nitrite made by the ammonia eaters.

Yes pH will go up with adding remin salts. You needed the KH high for cycling but as long as you keep the KH as around 3 you should be OK once the cycle has finished. Water changes will help replenish the KH. Since your tapwater has a very low KH, you might need to add a tiny amount of remin salts to keep the KH at 3, but it won't take much so it shouldn't affect the pH very much.

As you add more fish the amount of nitrate being made will increase. Nitrate and some of the hormones made by fish are acidic. The more there are, the faster they will use up the KH, so I would keep an eye on your pH regularly.
When I first had fish I was quite lazy about water changes. We didn't have internet access back then and twice I had an unexplained tank wipeout. The last time was 2002 - I remember the date as it happened the week after we had double glazing installed. I now suspect that it was because I was only doing water changes every 3 or 4 weeks, and I was overstocked. This made a lot of acid and allowed it to build up in the tank, which exhausted my low KH and dropped the pH dangerously low. And I didn't test the water back then either.

When you get more fish, add them a few at a time so you don't overwhelm the filter bacteria. Wait at least a week between additions and make sure your ammonia and nitrite stay at zero for that week.

This is all sounding good.

As for water changes.... that depends on the differences between the water you're adding and the water in the tank. If you find that you need to add remineralising salts and that this does cause a pH change, then you might be better off doing two 5 litre changes per week rather than one 10 litre change, depending how big a difference there is.