Tori-kun Wrote:④には ?? I found には expressing "in order to" also once but cannot find the example sentence right now..
It can be useful to break down such double particles and think about what each particle is doing in a particular sentence. には is used for emphasis in some sentences. When it means "in order to", I think of it as Purpose に + は (sentence topic/contrast/discourse topic/emphasis?).
に alone can mean "for (the purpose of)".
この辞書は漢字の勉強にいい。 This dictionary is good for studying.
Here, Vるには is topic and has Vるためには meaning:
食べる
には皮をむかねばならない.
To eat it, you have to peel it. (Kenkyuusha)
Purpose のに is [(usually action) V non-past + nominalizer の + purpose に] ("for the purpose of doing".) From DoBJG (p. 336 note 2): の is often dropped in conversation when 'noni' clause is topic, so ~Vるのには → ~Vるには.
すくやきを作る
には、何が要りますか。
What do you need to make sukiyaki?
Is that what you had in mind?
btw, for your list, there's also [V(masu stem) ni motionV] (see 'ni5' in DoBJG). Note that Nする (eg. 勉強する) can be either 勉強しに行く/来る or 勉強に行く/来る ("come/go to study").
I'll post a separate response to #1, Tori-kun. I started writing about "は and emphasis" and got a bit carried away...