Will the male and female terminals that you sell for your standard .100" rectangular and servo connectors work with these LP housings?

No, they're a different format and won't snap into the housings. The terminals & housings from the different families are not compatible in either direction.

Will a finished female connector made with your standard .100" rectangular and servo connectors plug into the LP male housings and header?

Yes, they won't have the locking or polarity features, but they'll plug together and make a sound electrical connection.

Will different size LP connectors mate with each other?

No, each size is uniquely tabbed so, for example, a 1x3 female connector will not plug into a 1x4 or any other size male housing/header because the polarizing tabs are in different spots. The only way a smaller connector could plug into a larger one is if the polarity tabs were cut flush.