The blasts are not counted as one of your moves, no. You're free to blast at will

Also, just so you know, I'm not teaching you character specific water techinques... There are a few that are only usable by Hozuki, Kisame, B, Yagura etc. Once we finish training you can use these techniques, but as they're not relevant until you have the bio I won't get you to go through them now.
This tech is nice, it's quick and effective if followed up on corretly. You swing your arm and cause the water beneath your opponent to rise upwards in a vortex, launching your opponent into the air. You can then dispel the technique at anytime you wish with another simple hand gesture (you can make it up... because... fun.)
Pretty niche technique this one, you manipulate water chakra within your mouth creating a whole load of water senbon which will fire out when you open your mouth. Pretty effective as a sneak attack, you can create the technique and then release then after a delay to try and catch your opponent out.