Could you explain what “David’s fallen tent” is in Amos 9:11 and Acts 15:16?

It refers to Israel.

Usually Israel is referred to as the House of David but the mention of a tent instead shows just how far Israel had fallen by Amos time.

We are beginning to see the restoration of Israel which became a nation in 1948 after almost 2,000 years of being in disarray. The final restoration will not be completely fulfilled until Christ’s coming and the millennium kingdom He will put in place.