1.can I say: 她吃饭得很多?
No, If you use 得 with separable verb, you have to either 1. Repeat the first part of the separable verb, e.g. 她吃饭吃得很多.(meaning she can eat a lot rice) 2. put 得 between the separable verb. e.g. "她吃得饭多" (meaning she ate a lot of rice or she eat rice very often)
"她饭吃得很多" has no separable verb (the only verb is 吃; 饭 is the object
讀書，唱歌，喝酒 are all separable verbs
她讀得書多，所以不怕找不到工作 (得 is inserted between the verb and object part of 讀書)
她唱得歌多，聲音也變得好聽了 (得 is inserted between the verb and object part of 唱歌)
她喝得酒多，說話有點含糊 (得 is inserted between the verb and object part of 喝酒)
她書讀得多，所以不怕找不到工作 (no separable verb, 書 is the object, 讀 is the verb)
她歌唱得多，聲音也變得好聽了 (no separable verb, 歌 is the object, 唱 is the verb)
她酒喝得多，說話有點含糊 (no separable verb, 酒 is the object, 喝 is the verb)
2.are degree adverbs needed?
It is optional
Both 我今天起得早 (I woke up early today) and 我今天起得很早 (I woke up very early today) are legit sentences