You are likely not entitled to any "home office" deductions unless you use the yard exclusively for business and never for personal use.
https://www.irs.gov/taxtopics/tc509
You are allowed to deduct "ordinary and necessary" expenses for your type of business. However, you can't deduct personal expenses. So when you have mixed expenses (lawn mowing, for example) you must separate the business and personal and only deduct the business part. There are two ways you can do this. One is to allocate the expenses using some rational method that you can keep records of. For example, if you have two personal pet dogs and 3 boarders, maybe you can claim 3/5 of the expense as a business expense. Another method is to use the "but for" rule. "But for the business, I would not have incurred this expense." The logic here is that you must mow your own lawn regardless of the business, so all lawn mowing is a personal expense, unless you can argue that your expense is increased by the business use--in which case you can deduct the increased cost caused by the business use. (I don't know which method might be used if audited, I have seen tax court cases go both ways.)
Permanent improvements are not expenses. A permanent improvement to real property (which means land plus anything permanently attached to the land) increases the cost basis, and is not deductible as an expense. If you perform landscaping, you can choose to treat it as an improvement to your personal home. This increases your adjusted cost basis which will reduce your capital gains whenever you sell. If you want to argue that part of the cost of the improvement is a business expense, you list that as a business asset and depreciate it over 39 years. In other words, if you spend $10,000 for landscaping or to upgrade your fence, and you decide half the cost is a business improvement, you list the fence as a business asset and you can depreciate it at a rate of $128 per year over 39 years. (You must also "recapture"--pay tax on--any business depreciation that you claimed on your home when you sell it, even if you otherwise qualify for the capital gains exclusion, so keep records of any depreciated items for as long as you own the house plus 3 years after you sell.)
However, be aware of the difference between repairs and improvements. A repair restores the property to as-was or as-is condition, while an improvement increases the value of the property or extends its useful life. A repair to a fence could be a 100% business expense if the damage was caused by a customer, or if it is a general repair, you might allocate a portion based on the proportional rule. A new fence would be an improvement and would add to cost basis and may be depreciated but is generally not allowable as an expense.
