What is the difference between 嫉妒，忌妒 and 妒忌 ?

Is "他的头撞在了墙上" grammatically correct? Why does the 了 come after 在 and not 撞? I've never seen "在了" before, and am wondering how to translate it into English. Thanks.

What is the difference, if any, between 导致，引起 and 产生 ?

What is the difference between 後　and 　の後に? For example, "朝ご飯の後に、出発します。" and "食べた後、散歩をしました". Don't they both simply mean "after"? Thanks

Can I use "AのほうがBより。。。" to express an opinion? For example, I know I can use it to say "中国のほうが日本より大きいです", which is a fact, but can I use it to say subjective things like "I prefer"? For example "魚のほうが牛肉より好きです" or "日本語のほうが中国語より簡単です"? Thanks a lot.

What are the differences between けれども, けど, けれど and けども? I think I'm right in thinking that these all mean essentially the same thing ("but"), and that they are just variations of each other, so I suspect the differences may be in formality. If you could confirm this and tell me which ones are used when, I would be much obliged. Thanks

In terms of politeness, how polite are 元気、元気だ、and 元気です? I'm just using 元気 as an example. My textbook says that a な-adjective on it's own is casual, but I have read elsewhere that a な-adjective with だ is casual.

How to I know whether to add -s or -es for the possessive case in German? For example, the possessive (genitive) case of der Freund is des Freundes, but if I hadn't looked that up, how would I have known that it ends in -es as opposed to -s? Is there a rule? Thanks a lot.

Why is ん sometimes added to ほしいです? I've seen this happen with a few other words as well. Is it because it makes the speech flow better?