It does not permit relicensing. You may use it in an aggregate work with other pieces that have a different license, including proprietary or GPL, but that does not mean your code is relicensed.
1. Its a good idea, if you are going to use licensed code that you have an understanding of the law and what it actually means when you use other people's code.
2. As the code is not relicensed you have to follow the terms. Generally for example even BSD licensed code (other than BSD0) requires that you include attribution both in source code and binaries or documentation, so you need to keep a full list of licenses and authors and list them out in the docs.
You can't take the code as-is and turn it into proprietary code. You need to build a derivative work that contains the permissive code plus some other proprietary stuff.
