Can I take a folding bicycle (no battery) about 16 inches (weight 7-9 kg) on board without paying extra?

You could transport your folding bicycle as checked baggage, not as carry on, but would likely be charged a fee. While the weight is within the usual allowance for baggage, its dimensions would probably exceed airline restrictions.

Your bike (or example), the Anchor, measures 22” x 29” x 12” folded and weighs 30 pounds. Generally, airlines do allow such items, but usually require they be bagged or boxed (and limit liability as a condition).

The only way to know for certain whether you can, and any fees, is to contact the airline.