The license is an agreement between you and your customers. It is not important if the library is commercial with $1M price or freeware. The person who has started to use it, got it from you (copyright owner). So, he/she is your customer. And, as a customer, he/she may expect something from you. To make these expectations meet your own requirements / thoughts, you have to have an agreement with your customer.
To simplify things, take some existing license text as a base for your own one. If in there you find something missing which is important to you, then just put that into the text. For example, you may give the full right to change the copyright text and redistribute the library as the customer wants it. Or you may prohibit that.
The library units are a part of your library. To make that clear for others, you may put a comment at the unit top. There you may say, "this unit is a part of the library Xxx. For more details check the license text". Or something like that.