好，is more informal。iIn formal conditions，以便于，为了 is recommended. Besides，好和以便于,can not start a sentence, can not say,下雨好用，带把伞。为了,can start a sentence, 为了挡雨，我带了把伞。

U r quite right. "好" can substitute 为了; 以便 ; 以 ; 用以 in most sentences, though its more casual. "好" has many meanings, so as to(以), in order to(为了), in case of(以免), so that(以便), ....

Yes, you are right. But it is more like spoken words than written language in Chinese.

我安装了wechat, 好让我练习英文。here 好 is similar to 为了; 以便 ; 以 ; 用以. 读大学好让我找工作。 for me, It expresses it is good to do something. but I think that is related to 以便,用以. you can translate as 便于，用以 等等。but it is not a definition. 别忘了带伞， 下雨好用。you can rephrase 别忘了带伞， 下雨以便可以用。 others seem not right. 今儿早点睡， 明儿好早起赶火车 rephrase 今儿早点睡， 明儿以便早起赶火车.

i prefer defining “好” “to make somebody\something or somebody\something to be in a good\better situation\condition”. for example ，"你好"，mean "u are in a good situation\condition","别忘了带伞， 下雨好用“,this sentences suggest that u will be in a better situation with an umbrella if its rain.Also this sentences suggest that u will be in trouble without the umbrella.