As far as i know the empire is weakened.Whats the situation in provinces in tamriel?Which are independent and who rules them?

The Empire is weakened, and consists of Cyrodiil, Skyrim and High Rock.

Cyrodiil is probably still damaged from the Great War.

Skyrim is currently in the midst of a Civil War, with the eastern half of the province supporting independence, and the west remaining loyal.

We don't really know anything about the situation in High Rock.

Hammerfell is independent; they would not accept the White Gold Concordat and so the Empire had to renounce the province. Hammerfell fought against the Dominion for five years after the end of the Great War, and eventually a treaty was signed and the Dominion withdrew.

Black Marsh is independent, ruled by the xenophobic An-Xileel party, which in turn is run by the Hist. The Argonians probably control some of southern Morrowind.

Morrowind is de facto independent from the Empire as far as I'm aware. It's still somewhat damaged after the Red Year and the Argonian invasion, and has probably lost territory to the south. The capital has moved from the destroyed Mournhold to the northern city of Blacklight. Morrowind now owns Solstheim, a gift from the Nords following the Red Year. There is still life in Morrowind though, and House Hlaalu, a major Imperial ally, basically lost all its power after the Empire left, and is no longer a Great House. House Redoran basically rules Morrowind now.

We don't know much about the situation in the Aldmeri Dominion, because they are so secretive. They are probably recovering from their own war losses.

We do know that Elsweyr has been dissolved into the two kingdoms of Anequina and Pelletine, which are client states of the Dominion, meaning they essentially obey the Dominion, despite not being an official part of it. Valenwood is an official part of it, and we don't really know what it's like there now. We know the Thalmor commit "purges" against the Bosmeri locals, probably killing those with impure ancestry. As for Summerset Isle, it is now called Alinor, and is ruled by the Thalmor. We don't know a lot more than that.