Interesting question!

The thing is, the Germans didn't know for certain that moving into Belgium would bring Britain, its large navy, and its small army into the war. The British Foreign Office and the Cabinet had been rather ambiguous in its foreign policy in the decade or so leading up to 1914. That waffling made at least some German leaders think Britain wouldn't honor the neutrality guarantee and intervene to help Belgium at all - the Kaiser later infamously called the guarantee a "scrap of paper" that Britain was foolish to fight a war over.

As for why they focused on France and not Russia.

https://i.imgur.com/KeJvPEX.jpg

1. Army size and capability - The Russians had the largest army in the world, (~5.9 million men in active service and the reserves) - however, limited railway infrastructure and supplies meant it would take months for the Russians to fully-mobilized. That gave the Germans a chance to try and finish the French and pivot to Russia before Russia could fully-mobilize. The French had a similar-sized army to the Germans (~3.9 million active duty and reserve French troops vs. ~4 million active duty and reserve Germans) and they could mobilize it just as quickly as the Germans. If the Germans ignored the French to focus on the Russians, they French would quickly mobilize and attack Germany before Germany could defeat the Russians and pivot back to fight the French. Which leads us to the next point...

https://i.imgur.com/ujHohks.png

2. Geography - the borderlands between Germany and France were populous and industrialized. If the Germans ignored the French, the French had a chance to cross the border and take these economically-vital areas. Meanwhile, the lands on the Russian-German were less-valuable and also much larger. If the Russians invaded (as they actually did in 1914), the Germans could afford to let the Russians advance a little before launching their counteroffensive.

https://i.imgur.com/Qbi5vZG.gif

3. History - During the Franco-Prussian War of 1870-1871, the Germans had been able to drive back and effectively destroy the French fairly quickly - the decisive Battle of Sedan was won in September 1870, and the war had only begun in July! In 1914, the Germans were hoping to repeat the same feat. By contrast, Russia, with its vast expanses and huge army, couldn't be defeated so quickly.