1. My husband is going to apply as the principal applicant. Do I (the spouse) have to present my former job's contract as well, or it's fine if only the principal applicant submits his ones?
No need for Contracts, but, better to submit your experience certificates so that it can be matched with your Personal History, and is proved that what you were doing (My Opinion).
2. Does the principal applicant have to present any document or any prove of his travels (IMM 5562)?

No... Just passport pages with personal details.