Can a woman go to the mikveh with hair extensions meant to stay there for a long time, in a permanent manner, the hair being glued with keratin. If the question is why she has extensions, then, perhaps because her hair is damaged or too thin. Or, even if she doesn’t cover her hair but is still concerned with niddah laws?
Having the hair extensions and glue in her is not l’chatchila for a married woman because of chatzitza issues, and most authorities would advise against her doing this for this reason. However, if she already has or if it is needed, then if the hair is in excellent condition, and the hairs nor the glue are cracking or falling out, then may go to the mikva. Additionally, if he hair extension is not meant to last for a long time then it would be a chatitza..
Igros Moshe Y:D 3-62, Poskim regarding nail polish.