Should one give gifts to those who one's close to, or those who one generally doesn't interact with very much?
If the professors who wrote my LORs seem reluctant to meet me again for some reason (not sure why - maybe they're just busy), should I simply forget about it?
Also, do people usually give gifts to their advisers for PhD programs, or not really?
This may vary from country to country, but I think a simple "thank you" is sufficient. Writing letters is part of their job.
I'm actually forbidden from accepting gifts from students, on the grounds that an outside observer might interpret the gift as undue influence. But then, I work for a state whose last two governors are in prison for various flavors of corruption.