Are למה and מדוע interchangeable?
Yes. מדוע is more formal.
No. למה is "why" and מדוע is "What is everything that you know (to make you think this, or whatever the case may be)?"
It's a much heavier word. Literally, "What is the knowledge?"
What does מדוע mean?
Lama atem meshakrim li. Madua atem meshakrim li.
Introducing new words is great, but they should come with audio.
Why not למה את משקרת אליי?
It's a heavier "why" than למה. Literally, "What is the knowledge?".
An older Israeli taught me that word is reserved for deeper, heavier issues. He said מדוע = What is everything you know that makes you conclude such and such?
is there a difference between לי and אלי? I thought the latter was to me...
From what I understand, אלי means "Towards me", while לי just means to me. אל means towards/to and ל is a modifyable to
To add, the preposition ל has a variety of meanings, including for and to