With regard to the differences b/w 「思い」 and 「想い」. It might be difficult even for Japanese. Normally「思い」 and 「想い」, as is noun, can use interchangeably and there is no differences in its meaning. But there are some differences in its usage. According to its Chinese character, 「思い」 means “think with one's head” (it consists of Brain and Heart). So it is very neutral meanings. Therefore, newspaper or public literature mainly uses 「思い」 for expressing their thinking. On the other hand, 「想い」 means “think with one's heart” (it consists of Tree as subject and to see with Eye and think with Heart. And old meaning is "Hope".). So 「想い」 is often qualified by some feelings, such as 「熱い想い」 = passion for/aspiration,　「長年の想い」 = longstanding ambition etc. So it totally depend on user, if user want to emphasis on some feelings, it can be used 「想い」. However it is not always true, for example, “one-side love” can be used both words, 「片思い」「片想い」. Might be confused?

Wow, dianthus's answer is very accurate. I'd like to answer the difference 「取る」,「採る」and「執る」. First, 「取る」means "pick up". It is used the most frequently. e.g. 「私はペンを取る」-> "I pick up a pen." Second, 「採る」implies "collect". For example, "have someone fingerprinted" in English means 「指紋を採る」in Japanese. Third, 「執る」means "head or lead something". e.g. 「政権を執る」-> "lead the government" OK?