How far ahead should I book?
For a wedding, months, and the good ones go first for Saturdays in summer. For a work lunch, often a week or two. Put the date in your request so only caterers who are free that day reply.
Is service and equipment included?
It varies more than anything else in a catering quote. Drop-off catering and fully staffed service are very different prices, so ask which the quote is and what hire is included.
Can they handle allergies and dietaries?
Nearly all can, but they need numbers rather than a note on the day. List the requirements in your request and the quotes come back already allowing for them.
What happens to the leftovers?
Worth asking, since food safety rules limit what can be sent home after being out at temperature. A caterer who is clear about it up front is one who takes the rest of it seriously too.