question about the verb "to close"

There is two questions i want to ask, one about the verbs and second about why they are all intransitive or if that's an error.

So i am studying my weekly kanji and kanji compounds and one of them is 閉. Now associated with this kanji i am given 4 verbs. しまる、しめる、とざす、とじる and all of them are classified as verb intransitive here(i think thats an error on my lecturers behalf, or if it is not please explain).
Now to the question, what are the differences between them and when are they meant to be used, is one meant to be used in specific contexts etc... It's all a little confusing. Also same thing with the verb "to open".

Those verbs are indeed confusing for non-native learners. Here's just a summary.

"閉[し]まる - 閉[し]める" and "閉[と]じる - 閉[と]ざす" are "intransitive-transitive pair". However, 閉じる is also used as a transitive verb. Similarly, "開[あ]く - 開[あ]ける" and "開[ひら]ける - 開[ひら]く" are "intransitive-transitive pair", but 開[ひら]く is also used as an intransitive verb.

Semantically, "あける vs. しめる" and "ひらく vs. とじる" are antonyms. Roughly, it's said that ひらく is basically only for "to open" when "to close/shut" is a set of actions (e.g. 本をひらく vs. 本をとじる). あける doesn't have this limitation (e.g. 缶詰をあける "to open a can"). Also, あける/しめる is for "two-dimensional " action, and ひらく/とじる is for "three-dimensional". There are some more differences but many exceptions also exist, so it might be better to remember the object and verb as a set.

○傘[かさ]を閉じる
×傘を閉める

○目を閉じる
○目が閉じる
×目を閉める
×目が閉まる

○花が開[ひら]く
×花が開[あ]く

Nice summary here. But it leaves me wondering, how opening/closing a door is a "two-dimesnional" action, since it uses 開ける／閉める? Or is it an exception? Similarly 目が閉じる appears as a two-dimensional action to me. I mean could you elaborate on that dimensions-related explanation?

"Linear movement vs. rotary movement" might be more appropriate. 開ける/閉める is more often used for sliding doors (e.g. 雨戸を開ける/閉める), and ひらく/閉じる is often for hinged doors. However, あける/閉める is more common for refrigerators even though they have hinged doors.
As for eyes, 目があく/目をあける is used as the antonym of 閉じる, and 目をひらく can mean "to realize" or "to be surprised(probably from 見開く)", not just "to open". There are so many exceptions, indeed.