1. I meant is it fine to say "I'm glad to get acquainted with you" instead of "it's nice to meet you". How will it sound like? Do you say it that way? This doesn't sound very natural. A native speaker wouldn't say it. 2. Can I use the word "acquaintance" like this, "I barely know Jenny, she's an acquaintance of mine but not a close friend"? Yes, that is how we use the word 'acquaintance'. 3. Can one say "let's get acquainted" or it's best to say "let's get to know each other", isn't it? Yes, 'get to know each other' sounds more natural. 4. Also, is it correct to say "we got acquainted at high school and still are good friends"? This doesn't sound natural. You'd say 'We met..' 5. And the last sentence "I never get acquainted in public places". This doesn't mean anything, I'm afraid.

The first would generally be phrased as "Pleased to meet you". The second phrase regarding Jenny is correct. For the third, either is correct, but most people would use "Let's get to know each other". For the next one, it should be "We met in High School, and are still good friends". And for the last, that is incorrect. I am not sure what your intent is for this statement.