"Fees" and "Bonuses" are income. Reimbursements are not taxable. Let me suggest you read through the "Sticky" above on "Taxes on Mystery Shopping".
Regarding phone calls. IRS works on the antiquated notion that 'everybody has a land line' and thus a first phone line into a home is not deductible. What can be deductible is if you need to make long distance calls, they are itemized on your bill and you can tie them into income producing shops. An easier way around this is to have a land line for personal use and a cell phone for your business. That makes the cell phone deductible.
Report time is a necessary evil and is already included in your shop fee, so there is no further deduction for that, whether it takes 5 minutes or 15 hours to write the report, deal with photos, receipts and all the rest.
But the equipment you use for your business is deductible--camera, laptop, printer, etc. These will generally need to be depreciated if not bought new and immediately used for your business. What you need is the original purchase date, price, when you started using them for your business and % of their use which is for business. Equipment such as this is generally expected to have a 'useful life' of 3-5 years but whether you are doing your return yourself with tax software or using a tax preparer you will need the same information.
Paper, ink and other office supplies you use are deductible.
The rules on a 'home office' are generally that it must be a space exclusively set aside for use by your business and no other activity. Generally a door that closes off the space from the rest of the residence is required. If your 'office' fits these criteria then you could be entitled to deduct the space and the utilities attributable to that space. So lets say you have a 1000 sq ft apartment and it has a 100 sq ft space that is your office. You would be entitled to deduct 10% of your rent and electricity. If you plan on going this route, talk with a knowledgeable tax preparer as every situation is a little different.
You can download a copy of a Schedule C from www.irs.gov/pub/irs-pdf/f1040sc.pdf to see what it looks like and the instructions for it at the irs.gov site as well.