First let me answer from the point of view of you owning the home.
You can deduct business use of the home if you use the home regularly and exclusively for business. Regularly means you don't have another place of business (like a store). Exclusively means that the area of the home being used for business is not used for personal purposes. Then you can deduct a percentage of your mortgage, property taxes, utilities and insurance based on the percentage of the home used for business. I assume you eat, so your kitchen is probably not used exclusively for business, but the bedroom office and a portion of the garage might qualify. Let's assume that is 20% of the available space. Then you deduct 20% of your expenses. The remaining 80% of mortgage interest and property taxes are schedule A personal deductions and the other expenses are not deductible at all. You also deduct an allowance for depreciation (wear and tear) on the home. You can't deduct extra utilities (such as more than 20% of your water bill) unless you have separate metering and can prove the amount used for business.
You can't take this deduction now because you don't own the home and your fiancé can't take the deduction since it is not his business. Once you are married, you can take this deduction because marriage means you are considered to own the home for tax purposes even if the deed is not in your name.
If you rented a house from an unrelated landlord, you can deduct a percentage of your rent based on the same calculation, and a percentage of utilities if utilities are not included in your rent.
If you rented just a bedroom and garage from an unrelated person and used that 100% for business you could deduct the entire amount as rent but it would be a regular business expense (as if you rented a store) and not the business use of home deduction. The landlord would be required to report the rent as taxable income.
The problem you will have is that your landlord is not an unrelated person. If the IRS audits you, they may have questions about how your fiance determined what your rent should be for business use of the bedroom and garage. The IRS might also suggest that the rental agreement was a sham to take an unallowable business deduction. And the IRS would expect to see that your fiancé was reporting the rent as taxable income on his tax return. Your tax savings would be mostly offset by his increased tax.
I don't see a legal way to deduct your expenses in your current situation unless your fiancé reports the rent as taxable income. But you might want to consult a professional tax advisor.
Phone and internet are considered as a separate proposition. You can deduct 100% of your cost as a business if you have a dedicated internet connection or a business only phone line that you pay. But if you have a flat rate service you use for business and personal use, there are two arguments. One argument (that I believe is more correct) is that you can't deduct anything since the service is flat rate and your business use does not increase your cost. The other argument is that you can deduct a percentage of your cell phone and internet cost, but only if you keep logs and records that show what percentage of the use (megabytes of data, minutes of calls, etc.) is business use.
