Question

there is / are

Answer 1

There is/are ... "there" (or "here") in this kind of sentence is actually not the real subject of the sentence. It is called expletive constructions (填补). The real subject is after the verb (to be). The rule of subject-verb agreement is: With these constructions
the subject follows the verb but still determines the number of the verb. That is to say
if the subject is plural
we use a plural verb (are
were). Both of your sentences have plural subjects
so we use plural verbs. (1) There are a bottle and a book on the desk. ==> A bottle and a book are on the desk. (2) There are an orange and o apples in the basket. ==> An orange and o apples are in the basket.
参考: grammar.cccm.edu/grammar/sv_agr
用is还是are是按所要表示东西是单数还是众数来决定 There (is/are) a bottle and a book on the desk. 这句的东西是a bottle单数...a book单数 there后是单数便用is了 There is a bottle and a book on the desk. There (is/are) an orange and o apples in the basket. 这句的东西是an orange单数..o apples 众数 there后是单数便用is了 There is an orange and o apples in the basket. 再加多几句 There are oranges and apples in the basket. There are oranges and a bannar in the basket. 英文文法有些是很直接(细微)的结构关系，文法不是讲求宏观的统计。
参考: 我没有reference但每本文法书都应该有这答案的