- Nothing in mathematics is ever obvious until after it is proven.
1.1 This is one reason English not being a CFG is not "obvious".
- A right-linear grammar can generate English, because a right-linear grammar over some alphabet, can generate all possible strings of that alphabet.
2.1 A right-linear grammar can generate all of the strings of English - it can actually generate more sentences than just the sentences of English. You can't just be concerned with whether a grammar of a certain type can generate a certain class of strings. The question has to be more specifically about exact generation. Can grammar G generate a certain class of strings, and not generate other stuff? Is it possible to generate English and only English, with some right-linear grammar? Or, can a suggested grammar also generate Mohawk? Or generate some other language? The supposed grammar does not succeed, when it over-generates - when it generates more strings, or sentences, than are considered allowable or correct, in the language.
2.2 The correctness of a formal grammar, or a theory of grammar, is that it generates exactly the sentences of a language L - no more, and no less.
- There is a reasonably easy-to-come-up-with solution to the grammatical feature you mentioned regarding noun-verb agreement for number (which @Draconis provides). But does this type of solution generalize to all human languages?
3.1 Shieber 1985 provides evidence against that context-freeness claim. Their argument comes from Swiss German data. And there is a similar argument proffered in [Culy 1985]. Their argument is based on data from Bambara.
- You can easily tell from inspection of a grammar whether it is context-free or context-sensitive.
4.1 But the reverse is not true: you cannot easily tell from inspection of a set of strings, whether or not that exact set can or cannot be generated by a context-free grammar. We don't really fully yet understand what kinds of languages can and cannot be generated by C.S. vs. C.F. grammars. At least when explained in ordinary linguistic terms.
4.2 We don't really know what kind of facts could constitute an "impossible language" for CF grammar. Though Culy and Shieber have given us some suggestions. In short, none of this is "obvious".