Before I answer your main question, I want to give an advance apology for not going into as much detail as I possibly could, nor for providing any sources. I am currently typing this in my phone with a busted hand, so if you or the mods ask for further details or sources, I will be glad to eventually do so when I have access to a computer. Also, I did not answer your second question, but I intend to get around to it eventually.

Scottish Gaelic originated as a result of Irish settlements in northwestern Scotland during the 4th century CE. At this point, Scotland was inhabited by people commonly referred to today as Picts, whose now extinct language very little is known about, though the commonly held theory is that Pictish was related to the other Brythonic languages (side note: Insular Celtic languages are divided into two groups: Q-Celtic or Goidelic languages, of which Irish, Manx and Scottish Gaelic belong to, and P-Celtic (Brythonic) which includes Welsh, Cornish and Breton).

Around the 8th century, continuous contact with the Pictish kingdoms results in Scottish Gaelic spreading eastward, as Dal Riata becomes first a client to the Picts, then merges with the Pictish kingdoms to form the Kingdom of Alba, replacing Pictish with Gaelic. Around this same time, settlers from Northern England begin moving into southeastern Scotland, and English remained a language particular to that region until the the establishment of administrative townships (burgh or "toun" in Scots). As a result of the establishment of the burgh, many English speakers moved further into southern Scotland, and Scots began developing from there.

With regards to the actual development of both languages, I would not be much help, as I am not a linguist, though I am sure someone on here may be able to provide some further information into the development of Scots and Scottish Gaelic.