New User Here. Can anyone tell me if a single task can have a different calendar than the rest of the tasks?

Example:
Notice to Proceed: 15 calendar days after award of contract. (7 days a week)
Mobilization: 2 work days. M-F
E&S: 10 work days etc M-F
End of Project: 90 calendar days after Notice to Proceed. (7 days a week)

I have to make a preliminary schedule with no fixed dates. Any help would be appreciated.

Yes, it can. However, it doesn't sound like you need a different calendar - just to measure the lags in "edays".

For example:

Contract award is the predecessor to Notice to Proceed. The link is Finish to Start with a 15 edays lag.

Edays lag will count calendar (not working) days.