As of Sunrise, yes, Firestar is leader of Thunderclan.
It is all a matter of opinion. He is still a very good leader to the clan.
Bramblestar
He becomes Thunderclan leader.
Bramblestar is the current leader of ThunderClan. He was made Bramblestar in "The Last Hope", after the death of Firestar, the previous leader.
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He might I don't think so. Firestar is going to die in Omen of the Stars so that means that Brambleclaw is in charge. But he does have all the traits of a good leader and he's gonna get an apprentice in the Fourth Apprentice so he could become deputy when Brambleclaw becomes leader.
He lost it when ShadowClan and ThunderClan were battling, Russetfur killed Firestar and Lionblaze defended his leader and killed Russetfur.
When Bluestar died saving her clan at the end of book 5.
Rusty was renamed Firepaw when he joined ThunderClan. Later, he earned the name Fireheart and eventually became Firestar as the leader of ThunderClan. So, in total, he had three different names in ThunderClan.
Yes, he becomes a ThunderClan apprentice, Firepaw, then a warrior, Fireheart, then Bluestar's deputy, then when she died protecting her clan he became leader.
Likely, unless he dies, but not yet. So far, Firestar is still leader.
Some of the notable leaders of ThunderClan in the Warriors book series include Thunderstar, ThunderClan's first leader; Thunderstar's successor, Owlstar; Bluestar, a legendary leader known for her wisdom and devotion to her Clan; and Bramblestar, who led ThunderClan during tumultuous times.