Strong context or spoken informal conversation can cause parts of sentences to be omitted, because the missing parts are understood. This can especially happen at the beginning or end of sentences.
What are you doing? (I am) Going to the park, I'll be back at 3pm.
Who is sick? My friend is (sick).
He found a stick and was walking around like he was looking for a fight. (He was) Scaring people. He finally ran into someone that he didn't like and beat him (with the stick).
When you say "There is no way X", you are emphasizing that X will never happen. It's an expression of strong denial. Typically emphasis is on the no way in this phrase, so much so that the there is can be usually omitted without loss of meaning.
In no way can substitute for there is no way in the examples just fine and is equivalent.
Note that there is no way is a complete sentence and can be a full answer to a question. In these situations it's not a good idea to use no way or in no way, it will sound weird most of the time.
Can you fix it? There is no way.
Can you fix it? No way. (Sounds weird, like you are being curt or overly terse.)
Can you fix it? In no way can I fix it. (Sounds like you are overemphasizing that you can't fix it.)