1st day of labor or materials. Can you confirm if this is the first day of labor onsite? We do design work that starts way before we are onsite. Just want to confirm which labor date I should be using. Same for material. We typically have the material shipped to our office and then taken to the site. Just want to confirm which date I should be using. Same for last day of labor/material. Should this be our final day of onsite labor?
Off-site design work by itself is not considered an "improvement" under Ohio's mechanic's lien law. Since that is the case, you should definitely use dates of supplying material to the project site (rather than material being delivered to your office) as the first and last dates of work for purposes of a mechanic's lien.
As for your last question, your first date of work and last date of work should be based only on the project, not labor/material specific, if that makes sense. Basically, your first date of work on the project (whether that was a date of supplying material or performing labor, or both) is your first date, and your last date of work (again, whether that is a date of supplying material or performing labor, or both) is your last date of work. You do not need to supply multiple first and last dates of work, as you can file one lien that covers both material and labor.
Correct. You should use onsite dates as the first and last date of work, as "work" in terms of mechanic's liens generally only includes work at the project itself.