Donations to Non-profit Organizations

The following is assuming you are the one traveling for the charity. If you are paying for someone else, I don't have an answer. 

Travel Expenses

Travel expenses are one of the most common deductions by volunteers. These include:

• air, rail, and bus transportation
• car expenses where travel is done by car
• taxi fares or other costs of transportation between the airport or station and hotel
• lodging costs, and
• the cost of meals.

If unreimbursed by the charity, such expenses are deductible if they are necessarily incurred while the volunteer was away from home performing services for the organization. A volunteer cannot deduct personal expenses for sightseeing, fishing parties, theater tickets, or nightclubs. Travel, meals and lodging, and other expenses for a volunteer's spouse or children are likewise not deductible.

Moreover, the trip must have been mostly for business, not pleasure, or it won't be deductible at all. The IRS says that a volunteer can claim a charitable contribution deduction for travel expenses only if there is "no significant element of personal pleasure, recreation, or vacation in the travel." This does not mean that the volunteer can't enjoy the trip, but he or she must have been on duty in "a genuine and substantial sense" throughout the trip. A volunteer gets no deduction at all if he or she had only nominal duties, or had no duties for significant parts of the trip.

2) No. 

This is not revenue to the charity.

You can deduct out of pocket expenses to pay to provide service to a charity.  The purpose of the trip must be substantially for the charitable purpose.  A vacation where you perform some charity duties will not count.  

"The deduction for travel expenses won't be denied simply because you enjoy providing services to the qualified organization. Even if you enjoy the trip, you can take a charitable contribution deduction for your travel expenses if you are on duty in a genuine and substantial sense throughout the trip. However, if you have only nominal duties, or if for significant parts of the trip you don't have any duties, you can't deduct your travel expenses."

Also, the charity must be registered in the US as an exempt organization.  Overseas trips won't be deductible even if the organization is a recognized charity, unless the organization has a branch in the US that is properly registered.