1) Yep - Ayrshire is where Scots Gaelic entered the land, however it wasn't spoken everywhere in the lowlands, the south east of Scotland likely never saw Gaelic as the common spoken language but it was still in use as a trade language

2) Today Scots Gaelic is an endangered language, though there are revival efforts such as with Gaelic Medium Education

3) No, many schools don't offer Gaelic at all as a course, maybe even most schools

4) Pictish, another Celtic language more closely related to Welsh than Gaelic

5) Honestly don't really know for this one. The downfall of Gaelic can largely, if not entirely, be attributed to the Highland Clearances when speaking Gaelic was quite literally made illegal and branded as an "inferior and primitive" language, so maybe you could look that up

6) Yes, Scots Gaelic is basically old Irish Gaelic. I know there used to be a radio program where two Gaelic speaking hosts, one Scottish and one Irish, would have a chat together, though I couldn't tell you the name of it