6 ft 1 in, often written as 6' 1", is the written form of 'six feet and one inch'. That's not what we say in conversation, however. In conversation, or as part of a longer text, I'd read that simply as "six foot one". Why 'foot' instead of 'feet'? I've no idea, but that's what feels natural for many people, myself included. There's also no need to say 'inch' or 'inches' (in the case of plural) : when we're talking about height, it goes without saying that the second number refers to inches. How tall is Tom Cruise? He's five seven. In other words, 5' 7".

It can be read 6 feet 1. I mean you don't need to point out that the second number is in inches. (It is understood)

That reads fine. This measurement is often written as 6'1". Remove the comma from before "could be so unsure" and it is perfect.

The 'five-seven' form is only valid if it is clear from context that you are talking about height, and therefore feet and inches. You could equally hear 'How heavy was your baby? / She was five seven', meaning five pounds, seven ounces.

US - I would probably say "Six-one." "How tall is that guy?" "Five-seven? Five-eight maybe?" If we know you're talking about height, the "foot" and the "inches" are understood. (of course, in the US, no one knows what 85kg means. :) )