First, you'll want to read this brief synopsis on the difference between prescriptive vs. descriptive approaches to language: Understanding Prescriptive vs. Descriptive Grammar.
(If you're interested in reading further, there is also excellent articles on the topic on the blog Polysyllabic and from the PBS series Do you speak American?.)
Now to the heart of your question. A prescriptivist might firmly believe that the only "correct" way to use those four words you listed (known as 'conjunctions') is in the middle of a sentence. But any descriptivist (i.e. professional linguists) would tell you that using conjunctions at the beginning of a sentence expresses is incredibly frequent, especially in spoken language. Try listening to friends' casual conversation or watching a sitcom and you'll be sure to find instances of at least one of those 5 words occurring at the beginning of a sentence.
Most commonly, it links to a sentence that another participant in a conversation has just said:
- A: I think that _.
- B: But haven't you heard that _?
It can also be used to link to something you have just said, separated by a pause.
- I think that . ( thinks for a moment ) And that's the reason why .
Prescriptivists are often focused on making the written language look/sound 'pure'. From that perspective, it makes sense why these sorts of things should be dispreferred in writing. In most writing, the first case above usually doesn't occur because only one person is writing. From the perspective of the reader, the second case above might come off as disorganized (under the assumption that the writer missed an opportunity to combine her/his thoughts into a single flowing sentence). Since it is so common in spoken language, another reason prescriptivists might say you shouldn't use it is because it sounds too casual/colloquial for many genres of writing.
So to sum up, breaking things into multiple sentences like this is perfectly normal and natural in spoken language, but prescriptivists recommend against using this structure in writing for various reasons. I hope that answers your question!