Did the wall temporarily halt Japanese advance or did they easily go through it using dynamite and/other explosives?

There appears to be some confusion here over the situation in China in 1937. This map here shows the initial Beijing-Tianjin campaign, in which we can see the first clashes of the Second Sino-Japanese War were all to the south of the Great Wall. Several Japanese units were already stationed south of the Wall before 1937. After the Boxer Rebellion in 1900, the Japanese China Garrison Army, around the size of a regiment, was created to protect Japanese interests at Tianjin and Beijing. It was a nighttime military exercise by the Garrison Army that triggered the Marco Polo Bridge Incident and the start of a general war. Additional Japanese troops of the Kwantung Army were stationed to the north of the Garrison Army in Rehe province (modern-day Hebei). The most famous sections of the Great Wall were in Rehe, including Shanhaiguan, long regarded as a key entry point from Manchuria into China. A major battle did occur over defensive positions along the Great Wall in Rehe - however, this was four years prior to the Second Sino-Japanese War when the Japanese launched Operation Nekka to annex Rehe into Manchukuo. So, by the start of the Sino-Japanese War in 1937, the Japanese were already holding positions south of the Great Wall, and the north-facing sections of the Wall had little if any strategic significance.

That is not to say the Great Wall did not have some tactical impact. When we think of the Great Wall, we often conceive it as a barrier facing north-south. However, there are some sections that face east-west. The east-west section of the Wall along the Taiyuan-Hebei border was garrisoned by both Guomindang and Communist troops when Japanese forces attempted to push west along the Beijing–Baotou railway. The GMD 7th Field Army under the leadership of Tang En-bo manned defensive positions along the Wall in the Battle of Nankou from 8 August to 26 August 1937. However, the Great Wall was an easily seen target from above, and the GMD troops were subject to continuous aerial bombardment. Political infighting further delayed the arrival of reinforcements, and with the fall of Zhangjiakou to the south, the defensive line was compromised and the 7th Field Army retreated to the Taiyuan area. The Great Wall did not have any major strategic and tactical significance after the initial battles of 1937.

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Sources:

Dryburgh, Marjorie. North China and Japanese Expansion 1933-1937: regional power and the national interest. Routledge, 2013.

Lovell, Julia. The Great Wall: China Against the World, 1000 BC–AD 2000. Open Road+ Grove/Atlantic, 2007.

Fan, Chang-jiang. Fan changjiang xinwen wenji [News Reportage of Fan Chang-jiang]. Beijing: Xinhua Chuban she, 2001.

Li, Ming-sheng. “Analysis of Japanese Strategy and Tactics in the Nankou Campaign.” Japanese Invasion of China Historical Research, no. 3 (2014): 99-105.