Modern Basque regionalism/nationalism dates back to the 19th century, starting as a broadly conservative movement in defence of the region's traditional rights against closer incorporation into the Spanish state. The autonomist Basque Nationalist Party (PNV) was formed in 1895, gradually moderating its initial traditionalist outlook as the region developed. Armed insurrection was limited in the 19th century to local supporters of a still more conservative tendency, Carlism, deriving from a disputed royal succession in the 1830s and combining acceptance of the old regional privileges with a deeply traditional social & political agenda. The Civil War of the 1930s thus paradoxically found the old adherents of armed struggle for the region's rights fighting on the side not of the autonomous PNV government but instead with Franco, no friend of regional rights. ETA grew not out of their tradition of rebellion but rather out of frustration at the PNV's perceived moderation. I think its radicalisation is a product of the Franco period rather than what followed, though support for independence has risen since, in common with other regions. Parties considered sympathetic to ETA's political goals (and sometimes banned as alleged political fronts) have won about a fifth of the vote in regional elections, though the PNV remains the largest party.

Another question, what are some good academic texts about basque nationalism?

Firstly, how far back can we trace 'modern' Basque Nationalism/Separatism? As in the roots of the current conflict, in say, the 18th or 19th centuries are there examples of Basque revolutionary/separatist activity?

Basque Nationalism was created by Sabino Arana in the late XIX. But it wasn't created out of nothing. For the most of part of the XIX century, there was a political conflict in Spain, Carlism. Carlism was started after the death of Fernando VII. Traditionally only men could inherit the spanish throne, but Fernando only had a daughter, Isabel, so he changed the law so his daughter could be the queen, instead of his brother Carlos. After the death of Fernando VII, supporters of Carlos -"Carlists"- didn't recognized the legitimacy of Isabel. Somehow, Isabel's side ended up favouring the modern european ideas from the Enlightenment, and Carlists ended up becoming a traditionalist movement that hated anything modern.

There was several civil wars during the XIX century, and support for the Carlist cause was specially strong in basque country and navarra (for basque nationalists, basque country and navarra are two parts of the same land), where the cause was also mixed with the defense of the special medieval political institutions that Navarra historically has had (Navarra was an independent kingdom that was annexed by force by Castile/Aragon in 1512). Carlists lost the wars, but carlism didn't disappear. Sabino Arana itself belonged to a carlist family. He created basque nationalism, inspired by other european nationalist movements, and it found strong support between carlists. It could be said that Carlism evolved to nationalism.

Secondly, after Franco's dictatorship ended and Basque's were given even more independence [...] Were the majority of Basque's happy with the new system or was there widespread discontent?

Basques thought that the current spanish political system was a clear improvement over the dictatorship, but for nationalists it still was a political system that they felt it had been imposed onto them without basques having a choice. After Franco died, the Basque Nationalist Party became the strongest nationalist party. There was a referendum in 1978 about the new spanish constitution, the Basque Nationalist Party pushed for abstention, and abstention got a 54% of the results.

what were the factors that radicalized some people and convinced them of the need for an armed struggle?

Note that ETA was born during the dictatorship. Also note that ETA is not just an organization that fights for independence, they fight for independence and socialism (ie. they are strongly anti-capitalists, although the anti-capitalist component diluted with the time)

For ETA supports, modern spanish democracy is a façade. They pretty much think that Spain still is a dictatorship and will keep thinking so unless an independence referendum can be celebrated.

Thirdly and finally, during the Basque conflict how much support was there for ETA's actions? Where they a tiny minority or did they have significant grassroots support?

It varies a lot. Only a very very tiny minority supports ETA today. But before the death of Franco, ETA was widely supported, not just between basques, but also for lots of people in all of Spain. Back then, ETA was seen by many as an anti-dictatorship organization and thus popular for anyone who was radically opposed to the dictatorship.

In the 80's, when ETA attacked politicians, soldiers and policemen (which were consider a symbol of the oppression), they were somewhat popular. They lost a lot of support when they started killing people like journalists or university professors.

Note that one of the main successes of ETA is not to be able to get support for their killings, but the lack of a strong, wide opposition against them - for a long time, the basque society didn't have strong reactions to killings (ie. policemen would be killed and literally nobody except the family would attend the funerals, people who spoke against ETA were marginalized, etc)