I bought a bmx with a 20x2.35 inch tyres on them, can i buy and put a 20x2.4 inch tyre on them without changing the rim and inner tube?
Look at the clearance between your existing tires and frame/fork. 0.05" is about 1.3 mm, so it means about 0.7 mm at each side. This is hardly noticeable difference. If your tires are not already dangerously close to rubbing your frame/fork, neither are the 2.4" tires.

Be aware, however, that manufacturer's measure of a tire is an estimate, and actual tire width depends on the rim width and other factors. Tires marked as 2.4" may in fact be narrower than older 2.35".

Inner tubes are flexible and can stand at least 2× to 3× variation in width. In your case, the difference is about 2%, so you'll be fine.

Similar goes with the rims. There are limits on how wide a tire makes sense to install on a rim of given width, but 2% of difference is just below error margin.