No idea what the brown spots are without a photo. May simply be natural variation, or may indeed be some kind of skin parasite. Because puffers are more tolerant of salinity changes than external parasites, either raising the salinity to SG 1.010 for a while, or dipping the fish in full seawater for 20-30 minutes two or three times, should do the trick. Standard copper-based medications are best used as a last resort with puffers than as a knee-jerk reaction.
Algae can't really be "stopped" in any meaningful way without rapid plant growth. In brackish water tanks where people tend not to grow plants, inevitably it ends up being algae removal the old fashioned way... with a scraper or sponge. I would suggest just letting the algae grow on everything save the front glass.
If that doesn't appeal, floating plants can work very well. Hornwort needs only moderate light to survive (1.5 W per gallon) though more light is better. It tolerates brackish water well up to about 1.003, maybe slightly higher if acclimated carefully. Hornwort is one of the best algae-busters. Being a floating plant, it looks very "seaweedy" in a brackish tank so can work well when coupled with driftwood, rocks, and shells.
No, ottos cannot be kept in brackish water. They're soft water fish, and even in plain hard freshwater aren't easy to keep.
Cheers,
Neale