Did atrocities like this happen among allies during the civil war?

The Spanish Civil War was incredibly violent, almost unbelievably so. Paul Preston estimates nearly 200,000 noncombatant deaths alongside a similar number of military deaths. Atrocities of nearly every conceivable kind were perpetrated by the constituents of both sides, and killing ostensible allies was not uncommon. Alliances during the war were tenuous things, because often you didn't actually like your allies--you just disliked them less than you hated your opponents.

The Spanish Civil War was dominated by circumstance.  It forced partisans of each side to support those they had no sympathy with. (Pg 206, The Spanish Civil War as a Religious Tragedy, José M. Sanchez)

It's not fully ally on ally, but one instance of an infamous atrocity is the Nationalists killing fourteen Basque priests for their political views. Now, fourteen people is not even a statistical blip when it comes to two hundred thousand noncombatant deaths. However, the fact that the Nationalists proclaimed that they were on a "crusade" to defend Spain from communism, and they had justified this idea by pointing out Republican anticlerical violence (which eventually claimed the lives of nearly seven thousand religious in Republican territory). So, the very class of people you set out to protect end up being executed by your own men. These priests were the Nationalists' ostensible allies--they opposed communism just as much as the Nationalists did, and should have been protected as noncombatants anyway. Executing these priests was the height of hypocrisy, and this incident alone should demolish the idea of a "crusade" by the Nationalists.

The aforementioned Sanchez and his Spanish Civil War as a Religious Tragedy touches on this incident, as does Mark Kurlansky in his The Basque History of the World. I just recently picked up Paul Preston's The Spanish Holocaust, which likely contains a good number of the atrocities in the first part of your question.

The Spanish Civil War had plenty of factional in fighting, especially with several violent clashes between supposedly allied groups. Perhaps the most notable of these flare ups in fighting - which Orwell famously described first hand in Homage to Catalonia - were the Barcelona May Days of 1937. A result of long tensions between anarchist and socialist elements of the Republic, as well as between the anarchists and the central government, the May Days saw violent street fighting between the CNT-FAI and their POUM allies, and the Popular Front government aligned factions, notably the UGT, PCE and PSOE. Over the course of several days, union headquarters and buildings were turned into fortresses, and the streets blocked with barricades.

Like the May Days, violence between nominally allied factions during the war were not uncommon, as the Republic was more of a vague and loose alliance of parties in the state and militias against a common enemy than a single coherent fighting force.

As /u/Domini_canes points out, interfactional violence was not exclusive to the Republicans either. The Nationalists also experienced a fair amount, although not nearly as devastatingly as the Republic, of in fighting and rivalry between the generals behind the coup as well as between the military and the falange, carlists and alfonsists.