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.)