My vague half-remembered understanding is that to make it 'We have read that newspaper' and 'We had read that newspaper' you'd need to add हैं and थे respectively. I agree that if you're presented with the English to translate you do need to see some kind of tense marker to know what's wanted as you can't tell without hearing it spoken.

Adding 'have' makes it past perfect, and it leads to a slightly different meaning than what it intended.

हमने अखबार पढ़ा - We read the newspaper. The sentence (in Hindi) usually indicates that something is to follow that statement. For example, हमने अखबार पढ़ा। फिर हम सो गए।- {Humne akhbār parhā, fir hum so gae} -We read the newspaper. Then we slept.

On the other hand, हमने अखबार पढ़ लिया है। {Humne akhbār parh liya hai} We have read the newspaper. This is usually a self contained sentence. You would say that to when enquired, "Hey did you guys read the newspaper?"

I know in English it sounds same. But in Hindi, there is clear distinction in past and past-perfect.

So the sentence in hindi is past tense "पढा" indicates past tense.