I am wondering when to use "way" and when to use "in a way".
For example,
1: I told you we should have done it my way!
2: They grinned at her in a friendly way.
3: Do it in the right way.
4: Do it the teacher's way.
Thank you very much!
Examples #1, #2, and #4 sound natural to my (American) ear.
Example #3 should be "Do it right." or "Do it the right way."
"In a way" is essentially an adverbial phrase. In example #2, it modifies "grinned at her".
"In a way" can also mean "kind of" or "sort of", which make a statement weaker or vaguer. It can be used informally as a "complete" sentence replying to a suggestion. When used as a reply, it is almost a dare to the other person to ask for more details.
"A way" is a path or method for doing something. For example, "The Way Forward." It acts like a noun.
"<something> is in the way" means that "<something> is an obstacle". My mental picture is of a person or a boulder blocking a narrow road.