Will unilateral orchiectomy lower my sex drive?

No, it shouldn't. Assuming everything went off without a hitch, your remaining testicle should be able to produce plenty of testosterone & sperm. Just to be sure, ask your surgeon to check your levels, preferably before & after. More likely, a decrease in sex drive or libido post-op can be due to stress (relationship, money, work family, friends), health, medications, substance use, as opposed to low t.
Possibly. Most people do fine after losing 1 testicle.