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But they could. That is exactly why they did know about nice atmosphere and water on the planet, but didn't know about the waves since the first wave that killed first astronaut happened during the landing. They also left one of the team member to do gravitation research and planned to spend as little time as possible on the planet.

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Yes, they knew about the relativistic effects. And they could obviously send some data. But somehow they can't figure out that they've been getting a repeat of the same ping for the last 10 years? And even if they couldn't figure that out, how could the person on the planet possibly send a ping every year, if she only spent an hour and half on it according to her frame of reference?

I don't remember how many pings they received in the movie. I've understood that they had received just one ping from that planet.

They expected a ping every year, if it ever stopped pinging they would write off that planet. It was up to the scientists to keep the ping going, if they considered the planet still a suitable candidate for humanity. The signal they received from the time dilation planet was supposedly "looped around the black hole" and repeated yearly.

If I remember correctly, one of the characters hand-waved it as (paraphrasing) "multiple echoes of the same signal". Meaning there were no meaningful timestamps

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