I don't eat it "recently".?

I've learned that the word "recently" should be used with past tence or present perfect. So it's correct to say "I don't eat it these days " rather than "I don't eat it recently ". But I found an entry on an online dictionary ; " Recently , though, she seems to have run out of energy." Question 1: Which is correct A) "I don't eat it these days "or B) "I don't eat it recently ". Question 2: can you say, " these days , though, she seems to have run out of energy." Thanks