Learn Portuguese (Portugal): Eu ainda não compreendo.

When saying 'still not' or 'not yet', Portuguese normally places ainda right before the negative word não. English puts 'not' first in 'not yet', but in Portuguese, ainda não is the standard order.

Do I have to include the word Eu at the beginning?

No, you can simply say Ainda não compreendo. The -o ending on the verb compreendo already makes it perfectly clear that 'I' am the one who doesn't understand. Using Eu just adds a little extra emphasis.

I've also seen the verb entender used for 'to understand'. Can I use it here?

Yes, absolutely! Compreender and entender are synonyms in everyday Portuguese. You can easily say Eu ainda não entendo and it carries exactly the same meaning.

How could I use an adverb of degree like muito or pouco with this sentence?

If you want to say 'I still understand very little', you would drop the não and say Eu ainda compreendo pouco. Because pouco is describing the verb (how much you understand), it acts as an invariable adverb, meaning it does not change its ending for gender or plurals.