You have gotten some great advice on here. You really need to get it out of the bucket as soon as possible. Your DT is no less cycled than the bucket but has more water volume which is important at this point. Use the clarifier that came with the sand. You can use the bacteria product you bought which will help, but as
@melypr1985 pointed out, it is a slower acting product. Biospira is a live bacteria product and works much more quickly. I would try to pick some of that up and use both products.
Very little bacteria is in the water so used or old water isn't helpful for cycling. It could be healthier for the fish since freshly mixed salt water isn't as well mixed as it looks. The fact you have some live rock will help immediately with the nitrogen cycle. The live sand won't help as much in the short term but it will provide some nice diversity for the bacteria and will help with waste removal.
You can use a regular ammonia test kit, you don't need the alert badge unless you plan on treating with copper. Don't worry about Nitrites. They won't harm salt water fish, that is a threat to fresh water fish.