Lesson 2.7 Question, Nouns Used as Verbs?

こんにちは (Konnichiwa) EarleyGrave, 

Thanks for your question. 

You're absolutely right! You can translate え (e) as "painting," "drawing" or "picture" and りょうり (ryōri) as "cooking" or "cuisine."

え (E) can mean "painting" or "drawing"  as in a completed piece of art, but it can also mean "drawing" or "painting," as in the art of making a drawing as a skill. Here it talks about this activity as a NOUN. If we want to talk about "drawing" or "painting" as a verb, we can use え　を　かく (e o kaku). 

りょうり (Ryōri) means "cooking" as in the art of cooking as a skill, not the verb "to cook." This means it is also a NOUN. The verb for "to cook" is りょうり　する (ryōri suru). 

Since we can only use が じょうず (ga jōzu) with nouns, we need to use the noun forms here. 
So what this sentence is really saying is:
"I am good at (both the art of) drawing and (the art of) cooking." 

If you want to talk about the action (verb) of cooking and drawing specifically, you can use の　が　じょうず (no ga jōzu) instead. You can learn all about how to use this grammar in this lesson:
https://members.rocketlanguages.com/members/japanese/lessons/5184/7-8-Doing-Things-With-No

I hope this helped! Please let me know if you have any other questions.
べんきょう　を　がんばって　ください！ (Benkyō o ganbatte kudasai!)