1.The Kingdom of the Picts (based in Fortriu by the 6th century) was the state that eventually became known as "Alba" or "Scotland". The development of "Pictland", according to the historical model developed by Peter Heather, was a natural response to Roman imperialism. The Kingdom of the Picts as it was in the early 8th century, when Bede was writing, was largely the same as the kingdom of the Scots in the reign of Alexander I (1107--1124).
(Note: The term 'Pict' is derived from the earlier Latin equivalent 'Picti' - which first occurs in a panegyric written by the Roman panegyrist Eumenius in AD 297 and is taken to mean "painted or tattooed people" (from Latin pingere "to paint", hence it's believed that the name was merely first placed upon the people of the land by outsiders, the Romans being the earliest ones to use the term).
2. 'Irish' is a modern English word, it is the Anglicised variation of the older Latin word 'Hiberni'. In Gaelige/Gáidhlig, you never refer to the language as 'Irish', ever. All modern dialects of Gaelic evolved from earlier forms of Gaelic/Goidelic, but were never ever called 'Irish', - the very term 'Irish' is first used from the 16th Century (1500's). In Gaelic, the actual word 'Irish' is literally translated as = 'Eireannach', and 'Scottish' is translated as = 'Albannach', but Gaelic itself is only translated as = 'Gaelige'. The Languages and the nationalities are never to be confused or conflated.
3. First off, to explain the commonly used term 'Gael' when it comes to this subject, the term 'Gael' was no more significant than what the term 'Viking' is, both meant the same thing, 'Raider'. The term ultimately comes from the ancient British appellation "Gwydell", used only to refer to the Scots. 'Gaels' did not "come to" Hibernia (From Gaul or from anywhere else) but the Scythians "came to" Hibernia of the Scyths/Scots of Dalriada (Argyllshire), when expanding their kingdom into Strathclyde, they were called 'Gwyddel' by the Brythonic speaking tribes, which meant 'raider', the [Scots] Gáidhlig word being "Gaidheal" which was later Anglicised into 'Gael'. "Gwyddel" was not applied to the Scots settlers of Northern Hibernia nor to Fergus mor Mac Erc but the Scots of Argyllshire. In Paul's epistle to the Colossians he talks about the Scythians (Colossians 3:11) whom are believed to have "come to Hibernia".
(Note: Dál Riata encompassed both sides of the channel, as Scots inhabited both sides of the channel, with Scotland by far having the vast majority, when you talk about the Scots of Dál Riata, you're indirectly/directly referring to Argyllshire and West Scotland by majority. There is and has never been any likely-hood that the Brythons called the Scots of Dalriada in the Ulster part 'raiders/Gael' if they stayed in Ulster. 'Scoti' doesn't mean 'raider' (As Rome's revisionists would have us believe). "Scotia" is merely the Latinised variation of the name (as is Scoti or Scotti) the word 'Scot' would be derived from 'Scythia'. 'Y-Scot' was a native British appellation, which is where the Romans got the 'Scotia/Scoti' term(s) from for use in the Latin language.