the reason your highlights came out that color is because you probably had layers and layers of color already on your hair OR your hair is naturally black...if neither of these was your situation, then the stylist clearly had no idea what they were doing and she have their licensed revoked.
if some look "greenish", this is from the toner they used to tried to use to cancel out the orange tones, but green doesn't cancel out orange, it cancels out red, so they should've used ash or platinum instead. the green probably stuck more to the porous areas. it will fade in a week or two, and wont be as noticeable.
as far as fixing it yourself?? well,, there really isn't anything you can do except dye it all brown at this point. you're not going to get blonde highlights without re-foiling it, which would require money and a hairstylist. you could try to go to sally's or your local beauty supply store (one thats open to the public) and ask what they recommend. without seeing your hair, i really can't tell you what color to buy.
you COULD go back to the salon and ask that another stylist (maybe the owner) fix it. just because one stylist messed up your hair doesn't mean another one will too. if you explain to the owner how unhappy you are with the color, they should fix it for you no problem. honestly, we dont want people to be unhappy with their hair. i know i would fix someones hair for free if i had messed it up.
as far as it being safe? well, im not sure of the condition of your hair, so i'm not sure what exactly a permanent color would do to it. if you think your hair is ok, then do it. if your hair is falling out or very fragile, i wouldn't recommend it.
i would wait at least a week before coloring it again. at least it'll give your hair some time to repair itself.
im sorry you had a bad experience! we're not all that awful, i promise!