Poor education and poor qualifications

People have poor education and qualifications. -- OK.
A woman has (got) a red handbag on her arm.-- OK. 'Got' is unnecessary, and an Americanism, I think.
People like walking around shops. (Along if it is a street market, for instance.)

Thank you for your answer, can I also say ..

People have a poor education and make education countable in this way?

People have a poor education and make education countable in this way?-- You wish to fix this sentence?

Not maybe fix I am just wondering whether it is possible at all to make a word education countable and how will the meaning change if we put an article a in front of education.

Yes, you can put 'a' before 'poor education': you have thereby reclassified the non-count 'education' into countable types of 'education'.

Ok, so to sum up when I say:
Can you help me to explain the meaning of the following sentences in details?

People have poor education- it means education in general or what does it mean?
People have a poor education - I mean one of many types of education in contrast to excellent education.

Thanks for help

layla

Can I say they distribute many fodders?

People have poor education.
People have a poor education.-- These both mean the same.

Can I say they distribute many fodders?-- Only if you are an agronomist and are discussing different types of fodder (hay fodder, alfalfa fodder, grain fodder, etc.)