Because the definition of a proxy war is when both sides are propped up by third parties. Otherwise pretty much every war is a proxy war of sorts.
No its not. I googled it, just to be sure. The results are not ambiguous. If I can Google it. So can you. Don't be lazy.
Post WW2 almost every war has been a proxy war between USA and USSR (including the civil wars). So you're not wrong about that. After the fall of USSR it got messier. But almost all wars continued to be proxy wars. Due to USA's great willingness to continually open their coffers.
USA's great willingness to keep funding wars, in the name of freedom, is nice, but pretty strange imho