I am doing business travel to Canada, and the travel agent wants me to send my passport number, home address, telephone numver, and birth date via email so she can book air travel. Should I send it? If not, how can she book my airfare?
All of the information they have requested is fairly common when making travel booking. Passport numbers and data of birth information is passed onto the airlines. Telephone number will potentially be passed onto multiple parties so they can contact you in the event of a problem (eg, delayed/canceled flight). And your home address, if nothing is, it the type of thing the agency will need for their own records and potentially for billing purposes.
If you are not comfortable sending these details over email, then I'm sure the travel agency would be happy for you to call them and provide the details - or send them your phone number and ask them to call you.