Heh, one of Irish false friends – in Irish An Bhreatain Bheag is ‘Wales’ (and ‘Brittany’ is An Bhriotáin, though historically an Bhreatain Bheag and Breatain na Fraingce – which would be written Breatain na Fraince in modern Irish orthography – had also been used, eg. by Keeting, while Wales was referred to by simple Breatain).
Yes. If you really want to do your head in, look at the names for all the Celtic nations in all the Celtic languages.
|Eilean Mhanainn||Oileán Mhanann||Ellan Vannin||Ynys Manaw||Ynys Manow||Enez Vanav||Isle of Man|
|A' Chuimrigh||An Bhreatain Bheag||Bretyn||Cymry||Kembra||Kembre||Wales|
|A’ Chòrn||An Corn||Yn Chorn||Cernyw||Kernow||Kernev-Veur||Cornwall|
|A' Bhreatainn Bheag||An Bhriotáin||Yn Vritaan (çheer)||Llydaw||Breten Vian||Breizh||Brittany|
|Breatainn Mhòr||an Bhreatain Mhór||Yn Vretyn Vooar||Prydain Fawr||Breten Veur||Breizh-Veur||Great Britain|
So 'Little Britain' refers to Brittany in Gaelic, and Wales in Irish, which is referred to in Manx simply as 'Britain', the term used in Irish for Brittany. Cornwall is referred to as 'Great Cornwall' in Breton as there is another one in Brittany. Bro-Skos is literally 'Scots Region'. Llydaw means 'Continent'. Manx seems to have attached the n from Yn to the beginning of *Albin and *Erin. You will see that Breton zh (pronounced /z/ in most dialects replaces the dentals t and dh/dd, so all the Brythonic languages have a similar word for Ireland. Cornwall seems to be masculine in Irish but it's not obvious why.
Try to learn that lot without getting confused. (All courtesy of Wikiepdia, so I do not guarantee they are right, and some may be disputed.)
The short answer is after Ptolomy.
It's nowhere near Dover which is in the SE corner of England. They spoke Anglo-Saxon in Dover at the time discussed here. Brittany is opposite SW England, from where Britons migrated at some time towards the end of the first millennium AD. That's why they call it Bretagne in French, which also refers to Britain. There is a lot of confusion in various languages from this part of the world about the names of all the Celtic regions and that is why Brittany is sometimes called 'Little Britain' and Britain 'Great Britain' in various languages. The Breton language is classified as a British/Brythonic/Brittonic language as it comes from Great Britain. It's closely related to Cornish and to Welsh, the language spoken in the the place referred to in Irish as 'Little Britain' and in Manx as 'Britain' (i.e. Wales). That makes it a first cousin to Gaelic. It has all the basic features you are familiar with: two genders, mutations (loads), continuous tenses, emphatic particles, verbs at the beginning, etc. etc. https://en.wikipedia.org/wiki/Brittonic_languages
If you want to see all the names the Celts have for each other, see my post on another question. It's a shambles. DaibhidhR