Is it possible to revisit the ‘Silent Realm’ after completing a trial

You won't be able to access them yet. The earliest you can would be your second visit to the forest...

after you have obtained the Water Dragon's Scale allowing you to swim. You'll have to climb the tree from the inside so you could drop down and reach those cubes.

The target you are referring to is a target for the Clawshots. These come even later in the game and allows you to zoom up to the target.

These are obtained by passing the second goddess trial.

In the challenges, there are 4 different types of things you could possibly win.

First of all the two most obvious things, Rupees and (mostly) rare Treasure. You can win these in either the Silent Realm challenges or the boss battles. Other things you could win in boss battle mode include a Piece of Heart after beating 4 bosses and the Hylian Shield after 8 bosses.

Here's the prizes you win if you stop in the boss rush:

1. 20 Rupees
2. Small Treasure
3. 100 Rupees
4. Piece of Heart (200 Rupees if you already received this prize)
5. 300 Rupees
6. Rare Treasure
7. 500 Rupees
8. Hylian Shield (1000 Rupees if you already received this prize)
9. 2000 Rupees
10. 3 Rare Treasures
11. 3000 Rupees
12. 9900 Rupees (Only possible in Hero Mode, since you won't have the option to fight Demise otherwise)