Yup. I use blue for clean water.
Maybe, maybe not. The nitrifying bacteria (ammonia to nitrite to nitrate) live on surfaces not in the water. So a good number probably made it into the sand.
If someone had mentioned giving you some bioballs or a filter from a nice tank, that will do a lot better at seeding the bacteria.
You can spend a lot of money on bottled bacteria and it won’t make it go faster. It will take 1-2 weeks to see the ammonia go down then another 1-2 weeks for the nitrite. Do not overdose the ammonia, 2 ppm only. Also do not test nitrate before nitrite is 0 as nitrite will give false high nitrate.
For cycling, I like the API tests. They are cheap, easy to do and many pet stores have them (petco, petsmart, etc).