The Government did not invent roads. Roads existed long before the Government made them, in fact most towns and cities had roads without a Government mandating and taxing people for using and building them. If you are referring to the Highway programs, those were not Federal Government ideas. Those were citizen and business owner ideas. The program went to the Feds because it was easy at the time, and saved States from having to negotiate connecting points.
The Government may have expedited some of the process, but we don't know how much because we only implemented one Federal highway program. In other words, it's impossible to measure help or harm from the Federal program. Did it add some benefit, sure, but you can't truthfully claim that it's all because of Government.
I'm not sure how many photos you have seen from the 1800s, back before the Government handled trash pickup, but I have never seen any that show giant trash piles in every lot. As with roads, trash pickup was happening without Government intervention as well. The Government didn't come up with concepts like "If you drink water with trash in it, it's not good water", we knew that well before a take over by the Government.
Your last example is the worst. Firefighters used to be all volunteers, and many fire departments still run on a measurable percentage of volunteers. Large cities collect taxes for dedicated people, and people can choose to live there or out in the sticks where they lack the services and don't pay the premiums. Believe it or not, Firefighting has happened in communities for as long as we have had communities without Government intervention.
In all of your examples, there is not a single case where you can claim that Government is needed. You can in some cases claim it adds benefits, but at the same time it's difficult to measure how much. Road building (construction in general) has, and historically has had, significant levels of political corruption.
It's impossible to provide hundreds of pages of concept in a post, so I'll recommend you read Stephan Molyneux or listen to his podcasts on anarchism. I don't agree with him on everything, but it's good for the brain to contemplate alternative opinion.