I have fewer concerns mailing things home. I've done it from China, Russia, and New Zealand without any troubles. Particularly true if you don't care when it arrives. Russia was very bureaucratic and a bit of a hassle to get the right paperwork. China in the Beijing post office was very efficient including English language instructions, packing materials, etc.

I haven't done medicines.

Again this is likely very country-specific and searching for that country and mailing will give a lot of information. There are expat communities living many places and they have those similar questions on getting things inbound.

When I thought I might want to beef up my sleeping bag, I did some searches about shipping to Peru. Amazon ships to many places and one could try "poste restante" to pick up at a general post office and pay duties there. There were also companies that give you a US address, bundle all the mail/packages together and then send to your Peruvian address. So it might all have worked...

However, Peru is also a popular destination for tourists to go trekking/camping up in the Andes. In the largest tourist cities there are some shops that sell limited outdoor goods - and even some places that will rent you the right trekking gear. So I figured (correctly) that it wouldn't be too hard to find something in Peru's second largest city, Arequipa, However, even before I got there, some cyclists coming the other way gave me an extra light sleeping bag they no longer needed (much appreciated).

That is Peru. Other countries will be different.