Yes, your sentences are absolutely correct. Slow in this case is not an adjective. It's an adverb. But to be even more precise, it is something called an irregular adverb. Irregular adverbs are not formed by adding -ly to the end of a word to make it an adverb as regular adverbs do. Instead, they follow their own irregular patterns. Some common examples of irregular adverbs include the adverbs hard (the adverb hardly is an adverb that means something completely different, by the way), fast and wrong, just to name a few:
If you want to become a fluent English speaker, you have to work hard on your English.
He runs faster than me.
Am I doing it wrong?
Notice that the adjective hard and adverb hard are actually two different words. Hard as an adjective means solid or firm. As an adverb, it means with a great deal of effort. The exact same thing is going on with the adjective slow and the adverb slow. Slow as an adjective means not quick. As an adverb, it means happening at a slow pace and is completely interchangeable with the regular adverb slowly:
He writes slower than me.
He writes more slowly than me.