This is a somewhat inaccurate definition. Socialism is the social ownership of means of production that does not necessarily mean the government. It comes in many forms such as democratic ownership by the employees (worker cooperatives), community ownership like utility providers being owned by the town and townsfolk, or state ownership if the state is democratically elected and accountable to the working class.

The concept of democratic and social ownership would be lost in an authoritarian state.

It has nothing to do with "Handouts". Or helping your neighbor really.

There is no redistribution of wealth. That is communism.

Socialism with handouts is communism.

Both socialism and communism are concerned with redistribution of wealth. They just disagree on the method. Socialists believe that by eliminating capitalism and with progressive taxation wealth redistribution becomes inevitable, whole communists thinks this will only be achieved with a powerful state to oversee the redistribution process.

You could have a completely Socialistic society that let's some of it's people starve because it benefits the majority.

This scenario contradicts the core moral and political goal of socialism which is ensuring the wellbeing of all member of the community by ending the exploitation inherited in capitalism. A system that allows this scenario is just unethical authoritarianism regardless of what people call it or think it is.

A great example to look at socialism is the nazi party creating Volkswagen.

The nazi party was socialist in name only. It was essentially a fascist regime that crushed actual socialist and communist movements, and imprisoned and murdered labour leaders. They also didn't nationalize the majority of industry and relied heavily on forced labour.

Again this fits state capitalism better than socialism. It's essentially the state controlling corporates instead of the social and democratic ownership by the working class that socialism seeks.

A large government can easily have a monopoly on a good or service.

For example, say America was 100% Socialistic.

Government would gain access to all satalites and towers and issue the Volkstelefon. Affordable phone and internet for everyone!

Imagine if tomorrow Trump issued his phone in that style.

thats a valid point but primary against state control not socialism itself.

In an ideal socialist system this Volkstelefon would be owned by a democratic entity rather than an elite group of politicians in a flawed democratic government. This entity would probably consist of worker and consumer representatives with the common goal of providing affordable high quality service that's also fair to both the workers and consumers.

Your concern here is also shared with most socialists.

While yes socialism can some time manifest itself in the form of state ownership that's never the ideal situation since it can easily transform into state capitalism if the state decisions weren't representative of the workers' will (which is usually the case in non-direct democracy systems).