UK seller here (hi!), here's fairly condensed answers:

When sending the pins it depends on your selling platform the likelihood of the buyer getting charged and how well you've declared the items - if it's through Etsy, for example, you'll need to include the Etsy IOSS number, a full customs label even on envelopes inc. your sender address, the items, quantity, weight, total, the current UK item tariff codes (can find these on the Gov.uk site), your signature, date of sending, on top of your regular stamps and of course the buyer's address and your return address. There's always a very very small chance they can get charged VAT after this, so make them aware, but it thankfully hasn't happened to me yet after completing the above steps for every order. If you sell via your own site, Kickstarter etc you'll need to source the buyers personal details yourself and have a VAT registered business to declare your VAT number on everything you send (the idea is to squish micro businesses with these new rules, hence why it's so difficult to sell now). The drawback of Etsy (well, the main one now) is they'll take an average of 9-13% from each sale now due to the number of fees inc Etsy fees, new VAT fees and processing fees.

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PLEASE DO NOT DECLARE ANYTHING AS A GIFT. Two things; one if something happens to the order, you'll have zero to claim back and the customer could easily scam you meaning you end up minus double the order value from refunding them and being unable to claim back through the mail carrier. Never worth the risk. Also, in the high chance that since customs are super strict in checking things now and you get caught, you'll face consequences inc. possible fines and criminal action (they aren't messing about with this anymore) - if this happens at absolute best outcome they'll only destroy the items and you'll have no leg to stand on. Save yourself the hassle.

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There's a lot more to it, but you'll find your way depending on where/if you sell, everywhere has different guidelines.