Will USPS pick up my packages for free, and does Media Mail count?

The rules on USPS's pickup page

“Your carrier can pick up your shipment for free during your regular mail delivery.”

“To schedule a free pickup for “Other” packages, you must have at least 1 premium service”

“Includes Parcel Select Lightweight®, Library Mail, Media Mail®, and Bound Printed Matter packages.”

The premium categories on the form are Priority Mail Express, Priority Mail, Ground Advantage, Returns (prepaid return labels) and International. DMM 507.7.1.3 agrees that a pickup made as part of a regular delivery or collection stop carries no fee:

“A package pickup that occurs as part of a regularly scheduled delivery or collection stop.”

What the carrier won't take

• “mailpieces weighing more than 10 oz bearing only stamps as postage are not eligible for pickup.” (USPS Schedule a Pickup page) DMM 507.7.2.2 adds stamped pieces more than half an inch thick; take those to a counter.
• Items over 70 lb or 130 inches, and anything without enough postage for the shipping and extra services.
• Hazardous materials not packed and labeled under USPS Publication 52; the form asks you to say which applies.
• Registered Mail and COD, which go to a Post Office clerk or a rural carrier (DMM 503.2.1.3 and 503.9.1.6).

“The United States Postal Service® bears no liability for lost, stolen, or damaged packages.”

USPS's page asks you to leave packages in a secure place your carrier can reach.

Pickup on Demand

• A pickup within a two-hour window on a date you choose, booked up to 6 months ahead at usps.com (DMM 507.7.2.6).
• Same day: “A same-day request for pickup must be made before 5:00 a.m. local time on the requested day.” (DMM 507.7.2.6)
• One fee per pickup, however many packages: “A customer is charged the required fee for each time Pickup on Demand service is provided, regardless of the number of pieces or combination of classes of mail” (DMM 507.7.1.2)
• No fee if you cancel within the rules, or with seven or more eligible pieces under a signed agreement with your Post Office: “A minimum of seven pieces of the eligible types of mailpieces in 7.2.1 from a customer who has an authorized signed agreement (Form 5543) with the local Post Office.” (DMM 507.7.1.3)
• Refund only if the carrier doesn't come: “You are only eligible for a refund if the carrier fails to show up during the specified day for a pickup.” (USPS refunds page)

Extra services on picked-up packages

Pickups can include Certified Mail, USPS Tracking, Adult Signature (not for certain items), insurance, Signature Confirmation and return receipts (DMM 507.7.2.3). For extra services, the acceptance evidence is the carrier's scan:

“however a physical scan must be received from the USPS as evidence of acceptance”

For insured packages that first scan matters: DMM 503.4.3.1 requires at least one USPS processing scan or your proof of insurance for a claim (proof of mailing).

Worked example: a books-only day