Ask HN: MIT licensed code, how to properly use when heavily modifying code?

I was curious about current best practices or legal guidelines to follow when working with specifically MIT licensed (to focus discussion) but potentially any OSS license:

The context is MIT Licensed code from another company/author than yourself.

1. Heavily modify code (to the point of being not-recognizable) that was originally MIT licensed.

2. Base new code off of ideas/patterns etc from an existing library.

3. Use a utility function or portion that is a small part of a larger library.

Are the answers different if the target/child project is MIT licensed completely or chooses a different license?

I think there are two sides to this question, both important, the community/proper way, and the actual/legal way to handle attribution, future licensing. I'm interested in both.

Thanks