Example: Screenshot from one of our boards - Crystal routing

2) I am not really sure what do you mean. Geometry of differential pair need to be calculated based on your stackup and should take minimum track width into consideration. Maybe you need to recalculate your differential pair track width and gap or possibly change stackup?
3) I always try to keep bigger gap around clock signals (usually as big as possible) - if you are not sure, I would go for 5H as the minimum gap (H is the distance from reference plane). We always try to route all the important signals (like clocks) inside PCB and between two solid grounds planes.
Examples of minimum track clearance

I am very happy the course helped you

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