Potatoes are large and dense. They hold a lot of heat. If you pick up a hot carrot, you can toss it from hand to hand and it will probably cool down just enough that you won't be badly burned. But a hot potato will stay hot for five minutes and burn the skin off your hand!
No. You divided the sentence incorrectly.
I strongly suggest that you post these questions on the Linguistics subforum, where they are appropriate, and where people who are interested in language and knowledgeable about language will try to help you.
For example, the executives of an energy company could appoint a well-known environmentalist to their board. This would suggest that they intend to make the company more "green" (supportive of the environment).
At the state and municipal level, laws ("statutes") can be enacted (often by the election tactic of the popular initiative, which is extremely common in California) which require members of the state, county or city government to be more responsive to their citizens and less responsive to the wealthy and powerful people in their jurisdiction.
Product warranties are often very weak. They may expire so quickly that the purchaser doesn't have enough time to decide whether the product is of good quality. They may have onerous requirements that make invocation of the warranty too much trouble to bother with. And they may limit compensation to such a small amount that they are ineffective.
No, you're wrong. This is a very common construction.
No. This is never correct. You can say, "She hated him because he was so happy."
There's really no important difference between these two.
This is an awkward way to form a sentence, although I suppose it is (just barely) correct grammatically. But it has a different meaning from the first two.
