Working on differents computer.

I really don't know many people to work with so i can't be for sure or i can't try to figure if you can work on another Mac with the same parameters in the plugins.

Hypothetically speaking If you rent a mixing room that works with logic pro and then you take the work home, it's going to be all exactly how i left it at the studio?

I know that if you don't have the same plugins you need to get the plugins but my real question is... The parameters you change on the plugins will be saved on the project file?.

And obviously the work will be lost if you don't have the plugin at home right?. (i know a solution for this though. Bounce)

I ask these question because in my country you can't be on the streets with a 1800$ Macbook pro.

Hypothetically speaking If you rent a mixing room that works with logic pro and then you take the work home, it's going to be all exactly how i left it at the studio?

Yes. The project file saves all the settings from your mixer, from the plug-ins you use in that mixer, it saves the position of the regions, etc... just make sure you take the entire project folder including the default assets (audio files). Meaning when you save your Logic project choose File > Save as and make sure "Include Assets" and "Copy External Audio Files..." are both selected.

I know that if you don't have the same plugins you need to get the plugins but my real question is... The parameters you change on the plugins will be saved on the project file?.

Yes, definitely.

And obviously the work will be lost if you don't have the plugin at home right?

You won't be able to use that plug-in at home, but the work is not lost. As you suggested, you can bounce to audio before saving the project at the studio to avoid the problem.