1.第二个动词都是用原形.
doesn't/didn't后面用的动词都用动词原形,而不能用单三/过去式,因为doesn't/didn't已经有了相应的单三/过去式变化了.
而且此时的动词2必须和and/or前面的动词1形式一致,因为and/or是并列连词,其前后形式必须一致.
如：I didn't dance or sing last night.
2.用are.
因为句子主语为复数（XX and XX ）,所以如果句子时态为一般现在时的时候,谓语动词的数也采用复数形式are.
如：Tom and Lucy are good friends.
3.没错,there be句型的be必须采用就近原则,即和最靠近be的名词的性/数保持一致.
如：There is a book and two pens on the desk..
There are two books and one book on the desk.