I learned that shi is used to connect two or more sentences. But sometimes I
hear it at the end of the sentence. What does it mean? Can you explain on
these sentences?

>   1. 濃くなってきちゃったら、部分レーザー脱毛に通えばいいし。
>   2. 穴があいた後ろから好きな当て布してもいいし。
>   3. 「ねえ、マッギー」「わたしマギーだし…」
>   4. 簡単にYou're right.とかHe's right.で良いと思います。または、論争していて相手の言うことを認めるみたいなときはOK,
> you win!でいいし。
>   5. あんな人のことは忘れたし！
>   6. せっかく来たんだからゆっくりしてけし。
>
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grammar conjunctions
し at the end of the sentence
As you have correctly understood, し **after the dictionary form** of a
copula/verb/i-adjective is usually used to connect two clauses. The first part
often works as the reason of the second part. In English it's like "and" or
"so", depending on the context.

If a sentence ends with し, it's either one of the following:

  * The "consequence" part is omitted because it can be inferred. It's like ending a sentence with "so".

> わたしマギーだし…  
>  But I'm Maggie, so...

The following part is something like "don't call me like that", but it's left
unsaid.

  * It works as the reason for the _previous_ statement. In this case it's like "(it's) because ...", "coz ...", "I mean" or "you know".

> 見てよ、面白いし！ Watch it, (because) it's fun!  
>  帰ろう。もう夜だし。 Let's go home. (Because) It's night.

If you are a beginner, you can stop reading here.

* * *

Your sixth example is different from the other five. #6 does not sound
particularly weird to me, but し **after the imperative form** of a verb is
recent nerdy slang mainly used on the net. (It's originally a dialectal
particle, but it somehow became a nationwide slang expression in the last 20
years or so.) This し emphasizes the imperative, like "hey", "yo" or "come on".
This usage is not in a serious dictionary, and you _should not_ use this
unless you really understand how it sounds.

>   * ゆっくりしてけし。 Make yourself at home. (slangy)
>   * 嘘言うなし。 Don't tell a lie. (slangy)
>
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Vita Holikina.

Concerning the "し" at the end of the sentence, it's usually hidden or omitted
a phrase or sentence. Japanese guess what is it from the context.

For example, （ ）is hidden and omitted in the sentence. This is an example.

Sentence #4: 簡単にYou're right.とかHe's
right.で良いと思います。または、論争していて相手の言うことを認めるみたいなときはOK, you win!でいいし。
_（そんなに難しく考えなくても大丈夫ですよ。）_

Sentence #5 あんな人のことは忘れたし！ _（もう、あの人がどうなっても気にならない。）_

Example:  
雨も降ってきたし…。（そろそろ帰ろうかな。）
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If I remember correctly, 「ゆっくりしてけし」is a dialect in Yamanashi prefecture. It is
equivalent to 「ゆっくりしていってください」「ゆっくりしていきなさい」.
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