How was Russia stepping in? I thought they provided equipment, "volunteers" etc. In what ways was the russian army directly involved during the period of all-out fighting?
At basically every key juncture.
The Izvarino pocket was created by a rebel unit seizing Saur-Mogila, but the destruction of the Ukrainian task force in the pocket was done by massive quantities of Russian artillery firing often from the Russian side of the border. The scenes of nearly apocalyptic burned out Ukrainian positions from that time period are the result.
At Ilovaysk 3 Russian btln tactical groups, at least one of them VDV, were the force that established both the outer and inner cordons around the mixed Ukrainian task force. The result was a brief negotiation followed by the Ukrainian party allegedly violating the agreement by trying to take heavy weapons and armored vehicles out of the pocket. The Ukrainian forces were then shredded by Russian fire in the process of trying to break out. 2 T-72B3 tanks were destroyed in the fighting, and one was abandoned by Russian forces, possibly due to battle damage or mechanical failure but the details are unclear. It was later retaken by rebel forces who (idiotically) displayed it to Russian state TV as a Ukrainian tank upgraded by the west (they didn't know Russian tanks had French thermals).
At the same time as the Ilovaysk disaster, a Russian mech unit entered Novo-azovsk on the Black Sea, towards Mariupol'. A Ukrainian National Guard btln column was dispatched from Mariupol' but either one or two trucks in the head of the column were disabled by anti-material rifle fire, after which they took sustained machine gun fire. The btln retreated in disorder, fleeing through Mariupol' (spreading some panic along the way). Novoazovsk is small and it's possible to keep things fairly quiet. However despite Mariupol' being left completely undefended no effort was made to take it. Likely because in a major city it would be too hard to hide that the entire effort is just Russian military. At that point no rebel forces were present in the area.
During the fighting for the Donetsk airport in the winter of 2015, continued rebel attacks led to them taking one terminal, the other still being in Ukrainian hands. Defense of the terminal was intense, and Ukraine managed to continue resupplying the structure, though at a considerable cost. Russian BM-30 Smerch MLRS were brought in at night, allegedly 2 of them. They were spotted and filmed by a civilian in Donetsk. They used allegedly thermobaric rockets, and completely annihilated the second terminal. Whjen the next day the rebels "took" the terminal there was no building left, no wall left standing, only rubble.
During the battle for Debal'tsevo sustained rebel attacks failed to close the pocket, and the town of Logvinovo remained in Ukrainian army hands. A Russian infantry unit, something elite maybe SpN or VDV, was used to clear the town, following which rebel infantry and reporters were allowed in, and the rebels claimed they took the town. Meanwhile the road to Artemovsk was cut by a Russian tank btln tactical group from the 5th Tank Bde. Wounded from the unit were later rewarded in a Rostov-na-Donu hospital, and footage of a column of T-72B3 tanks was even taken by the famous/infamous Graham Phillips.
These are just a handful of those that are too large to deny.