Is it safe to get my hair died while I am pregnant?

Yes. As long as you are in a well ventilated room.
Yes. Re: hair treatments — there are no good studies on occasional use of hair products during pregnancy. Exposure to hair dyes or hair products results in very limited systemic absorption, unless scalp skin is compromised by disease (eg, burns). Therefore, these chemicals are unlikely to cause adverse fetal effects. If you are working in a hair salon, wear gloves and work in a ventilated area.