Nationalist forces were composed by the bulk of the land army, a part of the air force and a smaller fraction of the naval forces. Besides that and theportuguese, italian and german troops, members of Falange, Acción Católica and the carlist Requetés formed militias early in the war. The manpower of those militias came mainly from rural areas in the northern half of Spain, with the carlists specially strong in Navarre and to a lesser extent the Basque Country. You have to take into account also that both sides drafted soldiera from the population in the areas they controlled, thus many combatants were not ideologically motivated or even had to fight for the side the didn't support (at least until they had the occassion to cross the lines) In the natiinaliat side, many old castilian peasants, generally conservativeareas (and those barelly republican were quickly executed in those areas, that is, Old Castille, Navarre and Galicia) werent behind the coup and probably would have stayed quiet in other circumstances, but once the war started many if them joined the nationalist armiees. Another key support for the bationalist, besides the big landowners, was the financial capital, with people like Juan March (the richest man in Spain at the time)and several banks funding the rebels. Formations like the Lliga Regionalista Catalana (the party of the catalan bourgeoisie) were also supporting the nationaliats, though they beitherwere behind the planning of the coup and joined latter.
And regarding wether you can win a civil war with smaller support, the nationalist advance over Andalusia and Extremadura, staunchy left-wing fiefs, shows otherwise, that when you have a proffessional army fighting armed peasants you can win even if your side is a minority. Spacially if you take care to reduce the numbers of oponents once you have taken the area (the Massacre of Badajoz, for example)
Regarding the internal factions in the nationalist side, tenssions existed, amongst the generals commanding the coup and amongst the different political organizations, with an special dislike between Falangists and Carlists akin to the dislike between Anarchists and Communists. Once Franco's position as Generalísimo was secured, his next step was the Decree of Unification, ordering all the militias and political.organizations to become a sole political party (Falange Española Tradicionalista de las JONS (Juntas de Ofensiva Nacional Sindicalista) or FET-JONS or also simply "Movimiento Nacional" ) which would be the One Party until Franco's death. So, their uniform was the blue shirt of Falange and the red beret of the Requetés. Of course many didn't like that and there was some exchange of fire and throwing of grenades amongst carlists and falangists, but an small scale. For this very reason, some of the opposition leaders in the 50's had been falangists (Dionisio Ruidriejo, Sánchez-Mazas...) and considered themselves "camisas viejas" (Old Shirts) in opposition to the "camisas nuevas" who had joined Falange after the unification. Also in carlist circles opposition movments appeared in this time, but I'm disgressing and I'm not sure if I have answered the question.
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