What can police do: indecent exposure accusations?

Yes

Exposure alone would have to be determined by testimony, but; why would they lie.

Why were they lured into his apartment?

What lured them into his apartment?

They would have probable grounds to see if this was done before and see if this person is a child molester.

Unfortunately, in my jurisdicition this is considered a form of sexual assualt and just an accusation is enough to get you arrested. It really depends on the officer you get. If the officer is a cvnt, then he will just arrest the accused person and not ask much question except ones that prove the neighbour guilty. If the officer is more fair minded he would ask questions to try to find the truth, if the neighbour acts like he might have done it, then he will arrest, but if he seems genuinely innocent then he will go interview the girls to see if they seem credible. If they admit to lying or get caught lying then the neighbour doesn't get arrested, but if they stick to their story and it is good enough to seem plausible/possible, then he will have to arrest and charge the neighbour, even if the neighbour was innocent. The neighbour would then have the chance to post bail depending on the serverity of the crime your charged with (depends what to lawyer/boss advising the officer tells him to charge you with). If your charge with a misdemeanor, you could get out the same day/a few hours, otherwise you might have to wait longer and pay more.

yes they can question him

but as a mother my 1st thought is wtf was my 9yr old doing in some dudes house and wtf was I at this moment..............

If the girls could identify something in his house then he would have some hard questions to answer