Short answers, pulled from the story.
The German invasion of Greece, known as Operation Marita, began on the 6th of April 1941 when German forces crossed the Bulgarian frontier at dawn. The broader campaign had started earlier with the Italian invasion on the 28th of October 1940.
Hitler decided to intervene on the 4th of November 1940, primarily to prevent British aircraft based in Greece from bombing the Romanian oil fields at Ploești, a critical fuel source for Germany. He also feared that continued Italian defeats would cause Fascist Italy to collapse and exit the war, which would allow Britain to reclaim access to the central Mediterranean.
The Metaxas Line was a system of concrete pillboxes and field fortifications built along the Greek-Bulgarian border in the late 1930s, running about 170 kilometres and designed on principles similar to the Maginot Line. The fortifications resisted the initial German assault on the 6th of April 1941 and held most of their forts until Thessaloniki fell on the 9th of April, after which General Bakopoulos ordered the surrender. The line was ultimately outflanked when the 6th Mountain Division crossed a 7,000-foot snow-covered pass the Greeks had considered impassable.
By the 30th of April 1941, about 50,000 Empire soldiers had been evacuated from Greece to Crete and Egypt, but the evacuation was heavily contested by the Luftwaffe, which sank at least 26 troop-laden ships. The Germans captured around 8,000 Empire and Yugoslav troops at Kalamata who could not reach the embarkation points, along with 7,000 British, Australian, and New Zealand personnel captured during the fall of mainland Greece.
Historians are divided on this question. The British Cabinet Office Historical Branch concluded in 1952 that the Balkan campaign had no influence on Barbarossa's launch date. Robert Kirchubel identified the primary causes of delay as incomplete logistics and an unusually wet winter. Antony Beevor, writing in 2012, noted that most historians accept the campaign "made little difference" to Barbarossa's outcome, though David Glantz argued it helped conceal the invasion from Soviet intelligence and contributed to German strategic surprise.
On the 20th of April 1941, Lieutenant General Georgios Tsolakoglou, commanding Greek forces in Albania, opened unauthorized negotiations with SS General Sepp Dietrich to surrender to the Germans alone, deliberately excluding the Italians. Hitler kept the negotiations secret from Mussolini, who responded by ordering counter-attacks against the Greek forces. An armistice including Italian participation was eventually concluded on the 23rd of April after a personal appeal from Mussolini to Hitler. Greek soldiers were allowed to go home rather than being held as prisoners, and their officers retained their side arms.