You sir are deep diving into what seems to be the wrong pool. DE shaving takes significantly longer than cartridges. Your soap, it's insufficient. The razor you mentioned in your post is generic. If you're shopping on Amazon, which is fine, stick to Merkur, Muhle, and Parker Razors that are closed comb, not open. Merkur 34C seems to be the most popular starter razor.

You change the blades as needed, Some change them every shave, others push 10-20 shaves. It's really dependant on your beard and preference for a sharp fresh razor. Most blades can be purchased on Amazon or eBay. Buy a good variety sampler pack to figure out what works best for you.