I would expect the 24" rim to be the same width as the 26" rim, which is 1.5" :
Your existing front tyre should simply transfer over onto the new rim to avoid having to buy a new tyre and inner tube, but if you really want to put a new tyre on it, most 24" bicycle tyres should fit.
Your existing tyre should have its size printed somewhere on the sidewall.
Although the rim is only 1.5" wide, it can still accept quite a wide tyre, as I have fitted 2.35" wide tyres on my 26" wheels and they fit nicely on the narrow rim:
I find the easiest way to remove the hand grips is to loosen the brake lever assembly on the handlebars and then use it to push the grips off the handlebars by pulling around the brake lever mounting bracket and clamp assembly.
If they are of the hard plastic variety, it may help to pour some hot water over the grips first.
Some soapy water usually helps the hand grips to go back on again, and the grip should be nice and secure again when the water dries.
Alan