"… things like this." vs. "… things like that."

I think what you're bumping into is not a question of grammar, but just an idiomatic usage. The only time 'things like this' sounds right to my ears is when there's an example in hand to compare to. And even then it feels a little awkward.

Gesturing toward the fruit basket, he said, "We're looking for apples, oranges... things like this."

I would say it depends on what the word "things" refers to. If "things" refers to the nuts and berries, I would always use "things like that", whereas if "things" refers to "leave and go foraging and gathering" – a common practise among foreigners – I would say "this" or "that" may be used equally. Using "that" would be the "default", if you will. And using "this" would be from the perspective that having just mentioned the action of "leaving and going to forage and gather" has brought the action to mind, as a concept to be held in one's mind thus warranting the use of "this".

Many times the same sentences may be correct with "this"/"that" interchanged where "that" generally will refer to the actual thing, and "this" oft times referring to its mental representation in a present conversation.