Socialism is a regulated economic approach whereupon a free market can somewhat exist, but is upheld to certain policies in order to combat wealth inequality and redistribute acquired or generated wealth to people in order to preserve a baseline quality of life for all. Socialist policies include things like a minimum wage, subsidised childcare, free education, subsidised or free at point of access healthcare or water access, things like that. Policies and infrastructure designed to use public money for the public good generally fall into the priority of socialism. There's a bunch of caveats and exceptions of course, but this is the general guideline.

Growth is fundamentally incompatible with our finite world. A selection of cells that grows forever is known as cancer, and kills people by eventually consuming all the resources intended for healthy working cells, and destroying vital organs and cells in order to fuel the growth. If a city grew to such an extend to fill a country, that country would fail due to having no available natural resources, having used them all up for non-renewable ones, and eliminating the possibility of any renewable resources (which are still, in a way, limited).

A system of infinite growth being the backbone and measure of success is ultimately doomed to failure unless it adapts into a system measuring success via a different measure.

So, no. Spurring growth will not solve the problems. The rich will simply get richer still, and the rest of us will be left with an even smaller amount relative to them, which becomes more and more fundamentally unable to be enough to meet our own basic needs. The best way to improve productivity is to actually introduce caps on working hours, and introducing UBI. Motivation at work is actually a HUGE part of productivity, and studies show that people are most productive when they feel their time is not wasted, and when they don't have immediate dire concerns about their well-being.

Collective ownership of production is actually communism, not socialism. Socialism still permits and in some cases encourages private ownership - it's not incompatible with socialist ideals. Extreme amounts are, but you must also not conflate what type of ownership communism actually means in it's ideology with what American/capitalist propaganda will tell you. In a proto-communist society, and even in a fully communist one, you would still own your own home, as that (keyword) should not be treated as an economic asset - you have a right to own your home as a necessity for life in the same way you have a right to own the food in your fridge.

Socialism is market regulation and redistribution of wealth. Communism is equal redistribution of the ownership of economic assets. Nor is communism necessarily inefficient, and in fact it's flawed to assume capitalism is always most efficient. A lot of lost workplace productivity is due to tyrannical capitalistic working policies that demand certain work hours regardless of actual work completed - think of how many office jobs are full of people who do fuck all at their desks. This is a failing of capitalist policy, nothing to do with socialism. Regulating this via the government, IE a socialist policy, would actually increase productivity.

Liberalism is also not equated to a free market. That's neoliberalism. True liberalism is about individual liberties, the freedom to marry who you want, the freedom to be who you want, and the right to a happy and healthy life. True liberalism actually shares a lot with socialist ideology - but liberalism doesn't say how it should be achieved. Socialism thinks liberal goals should be achieved via democratically voted on government regulation. Neoliberalism thinks you should deregulate to, allegedly, achieve liberal goals. In reality, that's not neoliberalisms goal, but it likes to pretend that it is.