Usage of に after verbs

Question

彼は川へ泳ぎに行った。 In this sentence, the 連用形 of 泳ぐ is placed in front of に, with the action verb 行く/行った, thus indicating the verb (to swim) for which the action (to go) is taken. My first question is if this construction (連用形＋に＋V) only works for action verbs (i.e. V must be of the likes of 行く, 来る, 帰る, etc.). I believe I read somewhere that that's the case, but on Japanese products I tend to see [連用形]に a lot—for example, a coat hanger might advertise itself with the phrase 「コート掛けに」. This seems to indicate to me that the use of [連用形]に to mean "to V" is not exclusive to those of such constructions followed by an action verb. If there really is requirement for an action verb in this construction, what's the difference between it and V1ためにV2?

Secondly, I have thought that whatever precedes に must be a noun (or 連用形, which—forgive me for my illteracy in grammar—I view as a pseudo-noun, if not a true noun). However, I've recently come across numerous examples of verbs in their dictionary forms being placed before には directly, e.g., 野球をするには寒すぎる. Is this a peculiarity of には or does the generality hold that plain-form verbs can come before に?

(Example sentences taken from ウィズダム英和・和英辞典.)

Answer 1

There is a rather huge difference in meaning and usage/function between the 「に」 and 「には」 that you are asking about.

「Verb in 連用形{れんようけい} (continuative form) + に + 行{い}く/来{く}る/帰{かえ}る, etc.」

In this phrase pattern, 「に」 indicates one's intent or purpose for going/coming/returning to a place. Thus,

「川{かわ}へ泳{およ}ぎに行った。」 means "went to the river to swim".

Regarding your question about advertisement phrases, it would be very difficult to speak authoritatively unless you told us what exact words followed 「コート掛{か}けに」. It could mean "Use this for a coat hanger!" or "Attach this (product) to your coat hanger (for a good effect)!"

「コート掛け」 would need to be treated as a noun rather than a verb in 連用形.

If there really is requirement for an action verb in this construction, what's the difference between it and V1ためにV2?

An action verb is a must for this construction to sound natural and complete. An important exception, however, would be when replying to a question like:

Mom:「何{なに}（を）しに川へ行くの？」

Boy: 「泳ぎに。いいでしょ？」

Both mom and the boy know that the boy is going to the river, so the boy does not need to use 「行く」.

The difference between the construction we are discussing and 「V1ためにV2」 is that the latter places more emphasis on the intent/purpose part (= the V1 part) and for that reason, the latter would tend to sound a little more formal and/or stiff. There is not really a difference in the basic meaning.

「Verb in dictionary form + には + Phrase」

「には」 in this structure means "in order to". This sentence pattern is usually used to describe how your plans/intentions/hopes might not realize because of what is stated right after 「には」.

「野球{やきゅう}をするには寒{さむ}すぎる。」 ("It is too cold to play baseball.")

This must be said with the dictionary form 「する」 and not the 連用形 「し」.

Answer 2

It seems that に can also be used for verbs serving as complements of verbs like "order", "promise", "force" also called control verbs in linguistics.

私 は 門 を 開けるよう に 頼まれた

'I was asked to open the gate.'