1. In general, capital costs for remodeling your office are treated as assets/improvements and are depreciated over time. Different types of improvements have different recovery periods.
https://www.irs.gov/pub/irs-pdf/p946.pdf
2. Depending on other factors, having your home in one state and your workplace in another state may subject you to a form of double taxation. If the two states have a reciprocal tax agreement, it may be simpler. But this is a situation where you need a professional to advise you before you get started.
Specifically regarding the overnight stay, since the shed/office will be your "main place of business", your travel expenses to and from your home are not deductible business expenses. The fact that the shed/office will have a bed for overnights (kitchen? bathroom?) does not disqualify it from being your office, but in some cases and for certain types of business arrangements, the fair market value of the lodging may be includable as taxable wages to employees. This is something you should go over with your accountant, assuming you decide to go through with the plan at all after discussing the state income tax situation.
Also, who is "we". If two or more people start a business, how it is taxed depends on the legal form of the business, who the owners are, and what state the business is located in.
