Group: In British English (and Australian/NZ English), a group can be either singular or plural, depending on whether you are considering it as a single entity or a collection of individual people. Both forms are correct. In American English, 'group' is a singular noun. The same goes for 'team', 'committee' and many other collective nouns.
Fish: Don't be confused by the irregular plural form. The plural of 'fish' is 'fish'. One fish. Two fish. You shouldn't use the form 'fishes'. You very occasionally see 'fishes' in technical texts to refer to species of fish, or in archaic texts such as biblical translations (loaves and fishes). But if you say 'fishes' in everyday contexts you will sound like a three-year-old child. Small children say 'fishes', and it sounds quite sweet, but adults just sound silly.
Your main question here is not whether 'fish' is singular or plural - it's an issue of whether the noun is countable ( in which case it has both singular and plural forms) or uncountable (in which case it only has a singular form). For example:
There are twelve fish in the pond. (plural countable)
John caught a big fish (singular countable)
Fish is healthier than meat. (uncountable)
Fruit: Again, this is an issue of countable or uncountable. 'Fruit' is usually uncountable, but - like most uncountable food - it can have a countable form when you refer to a type of fruit.
Fruit contains a lot of vitamins (uncountable)
Have you heard of a fruit called a durian? (singular countable)
'The fruits of your labour' ( plural countable - used in a figurative/idiomatic sense).