Nitrate is a bit on the high side - it should really be kept below 20 ppm. However, there may be quite a lot of nitrate in your tap water so you need to test that as well. If your tap water nitrate is above 20 ppm there is little you can do to get it lower, though using lots of live plants could well help.The only other alternative for reducing the nitrate in the water you put into the tank is to prefilter it with nitrate removing media.
Your high GH and KH are consistent with your high pH. KH is not important except where it is very low when it can get used up and allow the pH to crash. With yours being high, you can forget about KH.
GH is very important to fish, and is often referred to as just 'hardness'. Your hardness is pretty hard, so you need to keep fish that like hard water.
Back to ammonia and nitrite - both of these must be zero or the fish will suffer harm. The 0 and 0.25 levels in liquid ammonia testers can be hard to distinguish, but anything over 0.25 is definitely not zero.
You said your pre-water change ammonia and nitrite were 0.5 to 1.0. With reading this high you need to do at least 75% water changes per day. In fact you should test every day and do a water change whenever the reading is above zero.
If you don't have any live plants, I recommend that you get some. These are your best friend while cycling. They will take up ammonia and unlike bacteria they do not convert it into nitrite, they use it to make proteins etc. Getting live plants should reduce both your ammonia and nitrite levels, and with enough plants they'll reduce them to zero.
Water sprite can be planted in the substrate or used as a floating plant, and when used floating is particularly good at removing ammonia. They also need good light and carbon dioxide both of which are plentiful on the water surface.