Yes, MacBeth, or to give him his full name, Mac Bethad Mac Findláech, would have spoken Middle Gaelic, the language from which both modern Scottish Gaelic and Irish Gaelic derive. He was king in Scotland from 1040 to 1057 C.E. At that time, Middle Gaelic was spoken widely across Scotland, although a Brythonic language related to modern Welsh was spoken in the southwest, a Scandinavian language was spoken in parts of the north, Inglis (the ancestor language of modern Scots) had begun to come into the south, Latin was widely used, particularly in religious life, and the Anglo-Normans were about to show up and bring French into a prestigious position in later Scottish courts.

MacBeth was part of the Cénel Loairn kindred, which held power in an area centered around modern Argyll. In the 6th and 7th centuries, this area was part of Dál Riata, a kingdom which encompassed parts of both Argyll in Scotland and Antrim in Ireland. The Cénel Loairn was already a prominent family at that time. By the time of MacBeth, the centre of their power had moved north. MacBeth was not the King of Scotland in the modern sense, nor was he the only king in Scotland at the time.

The Gaels placed high importance on the role of the fili, a poet/historian/geneologist/storytellerwho was highly educated. These poets often went to Ireland for traning and the Gaelic intellectual elites maintained strong ties between Scotland and Ireland until the early 1600s, when the English invaded Ireland.

As you can see, Scotland and its courts were multi-lingual throughout the medieval period, and English gained prestige while Gaelic lost prestige, and the idea of Scotland as a nation coalesced. In 1609, the statutes of Iona required Gaelic-speaking nobles to send their children to English speaking schools. Some Scottish nobles were certainly bilingual in Gaelic and English well into the 19th century, if not the 20th (that's beyond my ken though.)

I can't fully answer the second part of your question. Margaret of Scotland, wife of Malcolm Canmore (the same Malcolm of the play), was English despite her epithet and has been credited with strengthening ties with England and kicking off a long process of Anglicization. Hopefully someone with expertise in that area will break down what happened and when.