Everything you have read about stative and dynamic verbs is true: verbs can indeed be divided into these two groups, and it's true that stative verbs cannot be used in the continuous aspect.
However, you have missed - or not been taught - one very important point: the verbs themselves are not fixed in one category or the other. There is nothing instrinsic to the verbs themselves that makes one verb stative and another verb dynamic - it's all about the meaning.
Most everyday verbs are fairly flexible in how we use them, and almost all verbs which are considered to be stative verbs also have an active meaning. In other words, so-called stative verbs are not always stative - most can be used in the continuous aspect to describe an action. Consider the difference between "Lemons taste sour" ( a universal truth and a stative use of the verb 'taste') and "I'm tasting the soup to see if it needs more seasoning" (an action taking place at the moment and a dynamic use of the verb 'taste').
Here are some examples of stative uses of 'have', meaning possess/contain, indicating states:
I have an older brother.
Do you have the time?
This drink has whisky in it.
And here are some examples of 'have' being used with dynamic meanings:
She's having her baby at Kings Hospital.
I'm having a party next Saturday.
John's having a shower at the moment. Can you call back later?
We're having dinner at 8 pm tonight.
I'm having a lot of problems with my laptop at the moment.
Sorry about the noise! My neighbours are having an argument.
I hope you're having a good time on holiday.
As you can see, these are all common, everyday uses of the verb 'have' to refer to actions and experiences. So, to answer your question, "May the verb 'have' be used in the continuous form?" Yes, of course it can!