An anti-hydrogen star - or even an entire star system - surrounded by normal dust would show annihilation events in the spectrum. So it would be very distinctive and unusual.
I guess so, if its electron/positron shell is the same. But I dont mean just antihydrogen. I'm sure there are many nucleus configurations that have the +1 charge and thus look like hydrogen from the outside.
But a larger nucleus would be unlikely to produce the same spectral signature even with the same charge. The energy transitions would be different, especially with different orbital shells and subtle quantum effects.