For the most part your statements are all correct. Its a little different if using the PVA client inside Teams instead of the regular Web PVA client. When in Teams a special environment is created in the Team when you create a new bot the first time. Everything created in that Team using either the PVA or Power Apps client will then go into a specific solution in that environment. In a regular environment bots you create are added to a default solution in that environment. So it depends on what the environment picker is set to where a new bot goes. But you can always create it in a specific solution by using the New Button in the solution.
Solutions are simply packages of items and dependencies that can be moved by exporting/importing them between environments. Its the best way to move things from a Dev to Test to Production environment. But there is no explicit way to set permissions at the solution level on the things inside the environment. Instead you set the permissions as you normally would on the Bot or database. There are permission settings that apply to what you can do with a solution, like import and export it.
In general then environments are a place where you can have a segregated space to control apps, flows, bots, etc. If the data source is Dataverse that will be specific to the environment also. If its something like SharePoint then its independent of the environment.
Solutions are a way to package up related components and move them from one environment to another. This is important because dependencies between components can become lost or broken if they aren't moved together. For example, if you have a bot that calls a flow and you don't move them with a solution you may need to re-add the flow to the bot after importing both in the new solution.
I hope that helps. Let me know if anything is still unclear or you have more questions.
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