Is it required that either all or none of the C fixed-width integer types to be defined?

The specification specifies the types int8_t int16_t int32_t and int64_t (and their unsigned variants) and follows them with:

These types are optional.

In C the type char is at least 8 bits and short and int are at least 16 bits and long is at least 32 bits and long long is at least 64 bits. If they are all at least a certain width and at least as big as the smallest one, there could very well be for example an 8-bit type and a 32-bit type but no 16-bit type while satisfying those rules. As such could be 'gaps' in the fixed-width types?

By 'These types' do they mean each one individually or all of them as a whole? Could a conforming implementation define some but not all of the fixed width types? Do I have to worried about for example uint8_t being defined but not uint16_t?

Is it required that either all or none of the C fixed-width integer types to be defined?

No. An implementation may have CHAR_BIT == 16 and so only defined (u)int64_t, (u)int32_t and (u)int16_t, yet not (u)int8_t.

Do I have to worried about for example uint8_t being defined but not uint16_t?

Don't worry about such unicorns.