Another newb with pics and need for help

[KPerkins]

We have had a tank for years, just moved this one across country. New sand, old rock, and one clown survived. (His name is now Marcus Luttrel aka lone survivor). After a month we got a couple new coral. Now they have white spots. We also had white slime, we cleaned it off manually and did water exchange. Pics of the white spots, and some white on my live rock. We also added a tang, gobi.

 

[Tahoe61]

Welcome to R2R. :-)

The last image looks like an area where purple coralline once grew and was either eaten by an invert, or the coralline faded and died back after changes in lighting and chemistry.
The images of the corals are blurred which makes it hard to be definitive on an ID. If I had to guess I would say probably some tissue recession related to swings in water chemistry, specifically alkalinity.