I like TV shows.

ii jya ne(long vowel sound) ka 　is manly way to say " ii dewa nai desuka" or "ii jya nai desuka", which means " Isn't it ok?". But I have to say it depends context : )

"abunai " is an adjective, which means dangerous. "abunaku" is also an ajective but used as an adverb. This means " nearly , almost". ( see also "ayauku") for example, I was nearly run over by a car----- Abunaku kurumani hikareru tokoro deshita.

First of all, we drop 私は a lot. You can say formally 私はイギリス人です, or just イギリス人です. " I'm from England" is 「わたしは　イギリスしゅっしんです」. "am" is not only translated into 「ます」or「です」. " I come from England" is 「わたしは　イギリスから　きました」. Both are pretty much same. We use 英国（えいこく）or イギリス for UK. イングランド→ England　　スコットランド→Scottland ウェールズ→Wales 北アイルランド→Northern Ireland

I have no idea about 量子力学、 but let me try. As paradox of cute cat, シュレーディンガーの猫 has become a reasonal keyword for introduction of 量子力学. or Using paradox of cute cat, シュレーディンガーの猫 has become a reasonal keyword for introduction of 量子力学. does this make any sense?

夜 is night, 夜間 means during night. You can say 「明日の夜、映画をみます」, but not　「明日の夜間」.

「大学をでる」- sounds "you were educated in college" . For example:「わたしは　大学をでていません」 means I don't have any experience of learning at college. I only have high school degree." 「大学を卒業する」- is, you finished and leave college. particle を is correct. ; )

Usually, we don't write むらさきin Katakana. Purple is パープル.