Yes. Albei and beide can both mean both.
So Ons gebruik albei kaarte is also possible.
A rough guideline:
So the sentence is correct as given, but learners will often hear albei too.
Afrikaans often does not use an article where English does.
In English, we often say both the cards. In Afrikaans, beide kaarte is natural without adding die.
You may sometimes also see beide die kaarte, but beide kaarte is already perfectly normal.
So do not expect Afrikaans to match English article usage exactly.
A rough English-friendly guide is:
Ons ≈ ons
gebruik ≈ guh-BRAYK or khuh-BRAYK
beide ≈ BAY-duh
kaarte ≈ KAAHR-tuh
A few notes:
The exact pronunciation depends a bit on accent, but those approximations are a useful start.
Yes. Ons gebruik beide kaarte is in the present tense.
It can mean:
Afrikaans often uses the simple present where English might use either the simple present or the present continuous. Context tells you which meaning is intended.