Something I use on all engine/cooling jobs is Sno Bowl. I know already .... Toilet cleaner YEAH! It contains HCL. Hydrochloric Acid. It will dissolve the "crystals" you saw. It is unusual to have a weeping condition after flushing the system on a brand new pump. You did see the corrosion on the outlet tho. That material had to go somewhere. It is in the engine. I would try using 2 bottles of snow bowl, and ride the scoot for at least five miles. it will start to foam out of the recovery bottle so you will want a rag to catch it before it stains any of the metal parts. Let the scoot sit for three to four hours w/ it in it, and then flush w/ a garden hose. Flush both ways. From top to bottom. and from bottom to top. I actually use Brick wash which is 100- 200 times more concentrated than Sno Bowl, but I don't want to see you or your scoot hurt. The timing is different w/ the wash. so DON"T TRY THIS AT HOME. I think you caught a piece of debris in the new pump. I also think it will work itself out. IF NOT at least you contacted the supplier to notify them there is a problem in paradise. On a PS note; Was that a rebuilt pump? Un - likely but had to ask!