Communism and anarchism are silly fantasies. The idea of having a stateless society is silly on its own, but the idea you can have a society with no rules (anarchism) or that if you achieved a level of post-scarcity production, people would need no "state" (communism) are just well, weird naive ideas IMO.
Um, no, fascism is not a "synthesis of left and right" whatever the hell that means. It's literally just a merger of state and corporate power, as Mussolini said.
"In fascist solutions, problems of unemployed labor and insufficient profitable outlets for capital (with the attendant economic stagnation and social conflicts) prompt massive state intervention. The state destroys or displaces the traditional leftist political parties and labor unions (often with violence, imprisonment and exile). It then substitutes various combinations of its own agencies (usually in the leading roles) supported by and integrated with nationalist and socially conservative parties and movements. Government leaders then organize close relationships with leading private capitalist groups to coordinate an "organic" direction to the nation's economic and social development. Those close, collaborative relationships organize full employment at wage levels that effectively guarantee capitalists' profits and government revenues. Fascistic government-capitalist relationships also manage the necessary tax structures, prices and currency values to support those objectives. Lastly, government revenues are coordinated with corporate production and investment decisions to serve fascism's non-economic goals (often military, diplomatic, nationalist, expansionary etc.)"
Fascism has nothing to do with unions/guilds so again not sure where this nonsense is coming from. Indeed fascists were anti-union and coined the term "privatization" because they believed in giving everything off to "private" owners.