The standard lease agreement from TREC has a sublet clause in it that makes a space for the amount of the surcharge than can/may require you to pay to sublet. My lease states the current tenant must pay $200 which compensates the landlord for running the credit check, re-writing a lease and accommodating any repair and maintenance issues for the new tenant. Additionally the lease has condition by which a landlord can accept or reject your choice of tenants. From a landlords point of view it will be a tremendous help to have the tenant find a qualified prospect to take over you lease. However your landlord will have the final say as to whether or not the applicant is acceptable.
It depends on the lease terms you signed with your landlord. Some require all that you've mentioned, a separate credit check and deposit. Others will just let you work it out yourself. Since it would be your credit on the line, you can choose to check the credit of the subletter or not, if you feel comfortable with that person. In that case, anytime the subletter defaults or walks away, you'll have to cover the difference.