I don't even think its possible to hate rice.

In addition to BJCUAI, I would say that 嫌い has a generaly negative feeling. You could say 好きじゃない and it would also be 'do not like.'

These are all very blunt ways to say dislike:

好きじゃない I don't like it

嫌い I hate it

大嫌い I really dislike it / hate it /don't like it

This would be more polite if talking about food:

Nounがにがてです。I do not like (noun)

Depending how you use it it can also be 'not good at.'

You can also use this verb when talking about people:

かれをにくむ I hate him / despise him

No. To hate is 嫌う（きらう）. To dislike is 好まない　（このまない）. きらい is a strong dislike, just as hate is in English.

It might be helpful if you gave a reason as to why you think that they were both represented as the same meaning, because they are not.

Japanese is a highly contextual language. As there is no reason to assume that the 'hated rice' is only the rice currently being served or only the rice at a certain establishment there would be no need to clarify which rice is being referenced; it becomes a blanket statement.

The fact that が is used here shows that the AはBが sequence is being used, with something being omitted. Again, as context has not demonstrated that anything specific is being referred to, the most likely construction would be: 私はごはんがきらいです - 'I hate rice'.

If in reply to the question: 'Of all this restaurants menu items, which do you hate?', it would make more sense for this sentence to have the second meaning you mentioned. Still, it would be unlikely for someone to phrase it such. It would be more common to say:

（私は）このみせのごはんがきらいです。

or

このごはんはあまりすきじゃない。/ このごはんはまずいです。

Grammatically, yes. In very casual spoken conversation it can be omitted, but this is not the manner of usage that Duolingo is aiming for.

nevermind, I found this article if anyone is interested: http://nihonshock.com/2010/02/particles-the-difference-between-wa-and-ga/ (apparently it's pretty complicated)

'Is hated' is 嫌われています.

米 is more common for uncooked/unprepared rice.