Check Scottish arms registry prior to application for arms?

Hi, I’m planning to submit an application for arms to the Lord Lyon. I have a design in mind. My surname is unusual, borne by only one family, and to the best of my knowledge a grant of arms has never been made in Scotland to someone with this surname before. The family did receive a coat of arms in England in the 1500s (I have not personally inherited these) and in Ireland (I have not inherited these either) slightly later. The Irish arms were based on the English grant.

My understanding is that in the Scottish tradition arms take influence from the original grant of arms (is this the chief of name and arms?) to that surname in Scotland.

So three questions:

1. How can I confirm definitively that nobody else with my surname has had a grant of arms before? I already checked the Public Register of All Arms and Bearings in Scotland online (no results).

2. Will my arms be treated as an entirely new grant without the need to be influenced by a prior coat of arms? (Would the Lord Lyon look for the closest Scottish surname to have been granted arms or seek to take influence from the English or Irish grant of arms perhaps?)

3. How does that work in respect of the Chief of Name and Arms? If my application were successful would I be recognised as a Chief of Name and Arms or is that only applied to those with a ‘following’?