Permission: The property owner might also consider giving the claimant permission to use the property and to get him to document this by signing an agreement.

You know - ask for forgiveness, not permission.

Do I I have to ask for permission from the IRS.

.§1.446-1, General rule for methods of accounting(c)Permissible methods(1)In generalSubject to the provisions of paragraphs (a) and (b) of this section, a taxpayer may compute his taxable income under any of the following methods of accounting:(i)Cash receipts and disbursements methodGenerally, under the cash receipts and disbursements method in the computation of taxable income, all items which constitute gross income (whether in the form of cash, property, or services) are to be included for the taxable year in which actually or constructively received.

You should bring to their attention that they rent from you, and they may want to ask for permission before making a big decision like that.  

Current tenant changed the front door lock without permission.

Should I give them permission for air duct cleaning or are there any red flags like if any injury or house damage occurs due to this who is responsible etc.?

@Mauricio Hernández The tenants cannot give you permission to do anything to the property, that's up to the property owner.

Since we will be entering hurricane season shortly, I need those branches cut/trimmed to avoid any major mishaps.I plan on sending a letter to the owner of the neighboring property but should I request permission to cut the branches off of her tree or should I just tell her that I will be cutting the branches?

And let's not talk about the clowns who will go and disturb the tenant without anyone's permission just to get inside and look at the house.