Our church choir is taking a trip and will be having several fundraisers. If someone underwrites the cost of food, beverage, etc. can they take that as a charitable donation? Also, if someone wants to donate money (NOT to a specific person, just for the trip, as a whole) is that considered a charitable donation?

Yes to both questions.

No doubt there are some rules about such things if you want a tax deduction

paraclete - what rules are you thinking about? Assuming teh OP is in the US, donations to a church are tax-deductible (within the limits of how much an individual may deduction as charitable giving on his/her tax return). The church should of course provide a receipt stating that no goods or services were provided in exchange for the donation, but other than that I see no issues here.

As long as the funds are being paid to the Church, and not given to a specific person. The church gives them reciepts for the donations and forwards the money to the choir.