Critical and crucial both have several meanings, but they can be synonyms - have a look at these definitions from dictionary.com:crucial
- involving an extremely important decision or result; decisive; critical: a crucial experiment.
- of decisive importance with respect to the outcome; crucial: a critical moment.
So you need to decide in which of your sentences they have the above meaning. With this in mind, my view would be:
1-The incident happened at a critical point in the campaign...
2-A critical situation is very serious and dangerous.
3-The German authorities are considering an airlift if the situation becomes critical...
4-Its day-to-day finances are in a critical state.
5-He took the crucial step of asking her to marry him
6-The next game is crucial – if we lose it we lose the match.
7-the crucial factor in their relationship was their unshakable faith in each other.
For the ones where I've said no, have a look at the definitions in a dictionary and you'll find that crucial or critical in these cases more closely matches another definition... Anyone agree or disagree?