Hi Ivy May,
I am not a language expert, but I'll do my best :)
1. Creativity tends to be used more for artistic things, and innovation tends to be used for inventions/technology.
2. Cultivate tends to be used to talk about crops and plants, or to talk about creating a specific atmosphere. For example, "The manager tried to cultivate good teamwork among his employees." Nurture tends to be used to talk about raising children.
3. I would say that obtain and acquire are very close synonyms. Acquire is used in certain specific circumstances. For example, you can acquire a skill set or acquire a language. Also, in the business world, when one company buys out another company, you might say that they acquired that company.
4. I think you mean "cater to." And it would be a synonym of "meet" if you are talking about meeting someone's needs. I use this expression, but I still couldn't think of how to explain it, haha, so this is the definition from Merriam-Webster, which I think is good: "to provide what is wanted or needed by something or someone." And I would add, to specialize in meeting the needs of a specific category or group. These are some of their examples: "The inn caters exclusively to foreign tourists." "The library caters to scientists." "As a child he was spoiled by parents who catered to his every need."
5. If something is intense, that means it is very extreme, no matter what it is. You can have an intense blue color, an intense flavor, an intense storm, an intense emotion, etc. If something is intensive, that usually means that it is very involved and detailed, and it's usually used with academics or other kinds of training.
I hope that helps! Those are great words to ask about :)