可以的。

需要 is followed by a noun or noun phrase in most cases. Ex: 他需要钱，很多的钱. (He needs money, a lot of money). 我非常需要你的帮助. (I greatly need your help .)But it can be followed by a verb or verb phrase when you want to be serious. ex: 我需要想一想。I need to think about it. In addition, 需要 can be a noun. Ex: 有需要的话，随时联系我。Contact me if there is a need. 要 is followed by a verb or a noun. 我要上班. I need to go to work. 要 is a verb, or a modal verb but NOT a noun.

没 is to negate an action in the past, while 不 is to negate an action in the present or future. I agree with the other answers.

I heard "How are you doing? " a lot!!

Both mean to travel. However, the purpose of 旅游 is to have fun, like 我喜欢旅游．(i like traveling) and 旅行 is more meaningful and rewarding, it has the meaning of journey. It's the difference between entertainment and experience. This is the reason why 旅行 can be used as a metaphor for life but 旅游 can't.ex: 人生是一次旅行。( Life is a journey). In addition, some words and phrases are set, like we say 旅行社　instead of 旅游社。