with 能作谓语吗？
你这句话是对的,只是这里with并不是谓语罢了
with表伴随后接动词什么形式？
这是 with 的复合结构
with 加 宾语 加宾补
宾补 可以由 非谓语动词 充当
可以跟过去分词
如 with his eyes closed
可以跟不定式
如 she was left alone,with no one to look after her.
可以跟现在分词
如 the old lived a poor life,with no one caring for him.
with表伴随的用法
with+宾语+宾语补足语，构成with复合结构，宾语可以是名词或是代词，宾语补足语可以是介词短语、过去分词、现在分词、形容词、动词不定式、副词。且with后面的宾语与其后的宾语补足语有逻辑上的主谓关系。
形式一 with+宾语+形容词
He often sleeps with the windows open. 他常开着窗睡觉。
Don’t speak with your mouth full. 不要满嘴巴食物说话。
形式二 with+宾语+副词
He stood before his teacher with his head down. 他低着头站在老师面前。
He was lying on the bed with all his clothes on. 他和衣躺在床上。
形式三 with+宾语+名词
He died with his daughter yet a schoolgirl. 他去世时，女儿还是个小学生。
形式四 with+宾语+介词短语
She said good-bye with tears in her eyes. 她含着眼泪说了声再见。
He was asleep with his head on his arms. 他头枕着胳膊睡着了。
形式五 with+宾语+现在分词(短语)
He fell asleep with the lamp burning. 他没熄灯就睡着了。
I won’t be able to go on holiday with my mother being ill. 因为妈妈有病，我无法去度假。
形式六 with+宾语+过去分词(短语)
He sat there with his eyes closed. 他闭目坐在那儿。
All the afternoon he worked with the door locked. 整个下午他都锁着门在房里工作。
形式七 with+宾语+不定式(短语)
I can’t go out with all these clothes to wash. 要洗这些衣服，我无法出去了。
With so many people to help us, we are sure to finish it in time. 有这么多人帮忙，我们一定能按时完成。
with后能不能接谓语
with 后面不能接谓语动词，只能接非谓语动词（不定式、现在分词或过去分词），构成 with 复合结构，在句中状语，表伴随、方式、原因、时间等。
With prices going up / the price to go up/ the prive gone down, people felt unsatisfied/satisfied.