What word does one use to record two people who are living together, not married, and may or may not have a child?

Partner and common-law are two choices. Non-solemnised marriage is another.

What is the best method to find children of relatives who hve died in the last 10-15 years?

First you must know when and where your relatives died. If you don't know start with the OCFA to track down burial information. Once you have a date and place you can find an obituary that may list names and places of children. You can then use 411 or telephone listings to track them down. Another option would be to contact the funeral home and request contact with the next of kin listed.

Where would I find passanger list for various ports?

See the The ShipsList Home Page for information regarding Ships, Passenger Lists and the like.