What fantastic, concrete advice, Jeremy! Thank you so much for sharing. I also loved seeing all your photos. When we travel, we, too, like to "live like a local" and shop in grocery stores, rent an apartment, and eat where the locals eat. We also limit ourselves to carry-ons only (which is much easier for a 2 week trip than it is for a year-long trip--kudos to you for being so minimalist!).
I would love to hear your advice about visiting non-English speaking countries. We relied heavily on Google Translate and pantomime but we were regularly frustrated trying to communicate with locals. I think that's why it's been easier vacationing in places where English is commonly spoken.