In English there are 12 cases of adverbial modifier.
Can all these 12 adverbial cases in English be expressed by Japanese particle に?
Are there other grammatical functions expressed by particle に?
As Sonny365 TANAKA mentioned, に can be applied to some of them, but not all.
Also, there're sentences which can be understood, but not natural with に.
I don't remember Japanese grammar well, so instead of that, let me translate them into natural Japanese for me.
1, 2, 3, 4, 6, 7, 12 are straightforward. Each of them has a corresponding expression.
The problem with 5, 8, 9, 10, 11 is that they don't have the perfect Japanese translations.
No.5 might be able to be separated into two sentences in Japanese.
No.8 says about the result. In this case, I learned in school that we can use this template:
「A して B する」
Using this, No.8 is translated into like 「それを光ら せて オフィスに飾りたいもんだな」
No.9 was difficult to translate. I feel like conditional adverbial modifier turns into just conjunctions both in English and Japanese. Separating an English sentence may be a good idea when you translate into Japanese.
No.10 contains comparison. Both of As if and As though are translated into 「みたいに、感じに、ように、かのように」in Japanese. These words are quite similar and all sounds like Like. So,
"She pretended as if she was the girlfriend of him" 「彼女は彼の彼女みたいにふるまってた」
"Your face is like a monster" 「お前の顔、怪物みたいだな」
See? Both translations contain「みたい」.
Btw, "I was like "What the heck are you doing!?"" is 「お前なにしてんの!? って感じだったよー」 in Japanese. 「感じ | みたいな」are really useful words. The same as I thought Like is useful.
I think the translation of No.11 is the same as No.5. Just separate it.
There're three にs in Japanese.
に the 格助詞 「机の上にある。」
に the 並列助詞 「魚に肉にデザートに、全部おいしそうだなぁ。」
に the 終助詞 「そんなに急ぐこともないだろうに。」
This is all according to this article. 格助詞 seems to be the one you mentioned in the first question.