It's not always possible to explain the meaning of a suffix. It's more important to know what function is has (ie, to change an adjective ' happy' to an abstract noun ' happiness'.)
'-ful' as a suffix originates from 'full', as in beautiful = full of beauty. However, as you can see from the example you give, this doesn't work for many of the words that now can be formed with 'ful' (Full of grates? I don't think so!) So here, the only clue you can give your students is to explain that it's an adjective ending. All words ending in 'ful' are adjectives.
'-ness' is an abstract noun ending.