”没“ vs. “没有”

“没” is a polyphonic character (多音字). When it's pronounced "méi", “没” has two meanings:

1. 没有（méi yǒu）

2. inferior to (e.g. “我没你高。” means "I am less tall than you.")

So when you use “没” as the first meaning, it means exactly the same as “没有”. But “没” is more colloquial.

“但” vs. “但是”

In modern Chinese they have the same meaning. However, "但" is mostly used in writing as a quite succinct way of expression. "但是" is frequently used both in writing and in daily communication.