A figure 8 simply keeps the horses mouth closed around the bit so it cannot evade the bit. Sometimes its used simply to keep a horses tongue in its mouth when the horse likes to stick it out. (Not kidding, there are horses that prefer to keep their tongue stuck out.) A flash noseband performs the same function but some people think a figure 8 is more comfortable for the horse.
You can certainly use a martingale with a figure 8. If you use a standing martingale be sure to attach it to the part of the nose band that does not go below the bit. It must attach to the upper noseband.
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You can if you're using a single bridle as opposed to a double/bridoon bridle. Double bridles have different requirements for bits and nosebands.
*Figure 8's are also called Mexican crossed or Gackle nosebands.