数 refers to the number of individual objects/things.
量 refers to the overall bulk amount of something.

Both can be measured.

○ バナナの数が300万個にまで増えた。
× バナナの量が300万個にまで増えた。
× バナナの数が300万トンにまで増えた。
○ バナナの量が300万トンにまで増えた。

In terms of your specific question regarding types of fruit, if you really wanted to use either 「量」 or 「数」 to refer to the number of individual types of fruit there are, it would be more appropriate to use 「数」, as you are expressing the number of individual types. However, 「種類の数が増えた」 sounds slightly unnatural/redundant, and we would simply say 「種類が増えた」.

番号 is simply a number that we humans have decided to give something for identification purposes or to express the order of something in a series.

数 refers to the number of individual objects/things.
量 refers to the overall bulk amount of something.

Both can be measured.

○ バナナの数が300万本にまで増えた。
× バナナの量が300万本にまで増えた。
× バナナの数が300万トンにまで増えた。
○ バナナの量が300万トンにまで増えた。

In terms of your specific question regarding types of fruit, if you really wanted to use either 「量」 or 「数」 to refer to the number of individual types of fruit there are, it would be more appropriate to use 「数」, as you are expressing the number of individual types. However, 「種類の数が増えた」 sounds slightly unnatural/redundant, and we would simply say 「種類が増えた」.

番号 is simply a number that we humans have decided to give something for identification purposes or to express the order of something in a series.

数 refers to the number of individual objects/things. 量 refers to the overall bulk amount of something.

Both can be measured.

○ バナナの数が300万個にまで増えた。
× バナナの量が300万個にまで増えた。
× バナナの数が300万トンにまで増えた。
○ バナナの量が300万トンにまで増えた。

In terms of your specific question regarding types of fruit, if you really wanted to use either 「量」 or 「数」 to refer to the number of individual types of fruit there are, it would be more appropriate to use 「数」, as you are expressing the number of individual types. However, 「種類の数が増えた」 sounds slightly unnatural/redundant, and we would simply say 「種類が増えた」.

番号 is simply a number that we humans have decided to give something for identification purposes or to express the order of something in a series.

数 refers to the number of individual objects/things. 
量 refers to the overall bulk amount of something.

Both can be measured.

○ バナナの数が300万個にまで増えた。
× バナナの量が300万個にまで増えた。
× バナナの数が300万トンにまで増えた。
○ バナナの量が300万トンにまで増えた。

In terms of your specific question regarding types of fruit, if you really wanted to use either 「量」 or 「数」 to refer to the number of individual types of fruit there are, it would be more appropriate to use 「数」, as you are expressing the number of individual types. However, 「種類の数が増えた」 sounds slightly unnatural/redundant, and we would simply say 「種類が増えた」.

番号 is simply a number that we humans have decided to give something for identification purposes or to express the order of something in a series.