Can we deduct cell phone bills if my husband uses his phone for work? And can we claim preschool bills as a deduction if Jennifer was not working?

Yes, you can deduct a business portion of the cell phone bill, generally speaking. You must somehow allocate between business and personal usage. 

How you report the cell phone expense depends if your husband is an employee or self-employed.

If he is an employee - he may deduct the business portion as a job-related expense if he is using the phone for the convenience of the employer... in other words, he may be required by his employer to use his phone. If he is only using the phone because it is more efficient/convenient for him - it is not tax deductible.

1. Federal Taxes
2. Deductions & Credits (you may have to select See all tax breaks)
3. Employment Expenses
4. Job-Expenses for W2 Income

If he is self-employed - it would be his "business" expense:

1. Federal Taxes
2. Wages and Income
3. Business Items, Select Business Income and Expenses - follow the interview questions; you would report the income as if you own a business; you will be able to enter your income and expenses (if applicable). 

Preschool - No, you cannot deduct the expenses, unfortunately. Jennifer actually must work or be a full-time student in order for you to deduct dependent care expenses.

 I understand how to allocate percentage use for the cell phone bill

My question is concerning the cost of the phone. Rather than paying for the whole phone upfront my provider is having me pay $40 monthly until the phone is paid off. Do I still deduct the whole cost of the phone up front (subject to percentage business use) as if i paid for the whole thing this year.

When i buy a laptop for my business I pay for the whole thing and take a section 179 deduction for the percent business use

If you are paying $40 a month for the phone then you should deduct your business use percentage of that $40 every month.