They were a minority in the country overall. They were a majority in the area of Kosovo, which has deep historical and cultural ties to the serbian national identity. That doesn't change the fact that like you said they were the obvious losing side in the war. Their most obvious patron was Albania, not exactly a powerhouse. And yeah, if NATO hadn't intervened, they wouldn't have won. They would have gotten ethnically cleansed.
Kosovo had autonomy, even then it wasn't that much connected to rest of Serbia. Serbia is pretty centralized country. Besides Vojvodina (another case of autonomy), Belgrade is pretty much the only place in Serbia worth living in, rest is just poor like Albania. Whole serbian national identity thing on Kosovo is bullshit and a myth. It is always an excuse but no one really believes in it.
I don't believe their patron was Albania. They are too poor to finance wars. Just like in civil war in Bosnia, support for muslim jihadist came from Iran and Saudi Arabia. They send the guns, money and support in form of their best mercenaries already proven around the world. That is why Vatican state never acknowledged Kosovo as independent state, because they see it as a part of muslim expansion in Europe which is what they truly believe in.
Also, don't think Milosevic's idea was ethic cleansing. He was a dictator who only cared about support. Obviously, he wanted to reduce numbers of albanian majority in Kosovo that way hurting future of guerrilla movements. But what I believe he really wanted to achieve with mass killining of civilians is to frighten albanians, showing them what could happen to them if they don't convert to his side and support him with votes. Bear in mind that at time he wasn't caring about anything nationalists wanted to hear and see, he just wanted to stay in the saddle for years to come. Nationalists in Serbia denounced him years ago before Kosovo thing happened, they even protested against him while supporting Chetnics.
You'd be surprised. That is the reason some serbs have gone to fight in Ukraine. It is perceived as some sort of payback for NATO actions in Serbia, which was a crime against "slavdom". Russia has been holding a grudge over what happened in Serbia for quite some time.
Some is right word, like no more than a dozen. While many Serbians are into that nationalist bullshit, most of them will never again participate in war because they felt it on their skin. Just barking, nothing more. And Russia isn't holding a grudge, they don't give a flying fuck about Serbia. They used the siltation as leverage. If they cared, they would defend Serbia from Nato in 1999.