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Sophia here from Shopify. Welcome to the Shopify Community!
USPS rates at checkout
It looks like the issue with the USPS rate appearing at checkout may just be the type of service selected in the shipping settings. The First Class Mail option is for letters and postcards, so it won't appear in the checkout unless your default package is set to an envelope within the size guidelines from USPS. Did you mean to select First Class Package option instead?
Free shipping promotion
There are two ways that you can set up free shipping within the Shopify admin. If this is an ongoing offer, you can create a free shipping rate under Settings > Shipping and delivery and specify that it applies only to orders $50 and over. If it is just a limited time promotion, you may want to create a free shipping discount code instead. The discount code will allow you to set a promotion start date and end date so you don't have to worry about changing your settings once the promotion is over.
Printing shipping labels
To print shipping labels from your admin, you can either use a desktop printer or one of the supported label printers. The label printers will allow you to print on the sticker paper instead of regular printer paper. If you don't already have a supported label printer, you can find printers and sticker paper in the Shopify Hardware Store.
Shipping labels for sample orders
I recommend creating draft orders when sending samples out to customers. You can skip sending an invoice to the customer unless they need to pay for shipping. Creating a draft order will allow you to print a label from the admin provided that you have the sample products set up with accurate weights.
I hope you find all of this information helpful. I've linked quite a few documents from the Shopify Help Center here, so please take some time to review them and let me know if you have any questions.
I'm following the direction you explained about creating shipping label for sending samples to the customer but I don't see any "print" mark on draft order.
You're almost there! Payment needs to be accepted for the order before the fulfillment options become available. If you mark as paid (provided you've already received payment elsewhere or no payment was required), the draft order will move to your regular orders list where fulfillment options including printing a label will be available. In this case, you can leave an internal note on the order indicating the original order number where the payment was accepted or that the order is for free samples, if that's helpful for your records.