How can I remove Finder and Trash from my dock (for Mojave) I've got my first ever Mac and was wondering how to remove Finder and Trash from my dock (and put them in Launchpad instead).

I've tried some of the solutions on other questions but they don't seem to work on my Mac.  Ideally I would like the icons to be removed automatically on start-up too.

Thanks :)
The Finder in MacOS is 'always on'. There is no need to Launch it in normal operation, so having it in Launchpad is fruitless. Any app currently running will normally appear in the Dock: so the Finder, being always on, will always be in the Dock.

The Dock provides functionality as follows: by right clicking on the Finder's icon, you can bring to the foreground any open Finder window, and perform other tasks like creating a new window or connecting to a server. You can also control whether the Finder is linked to a particular display or Desktop space. 

Right-clicking will also show if the Application is Not Responding, in the event of a problem, and is a useful troubleshooting technique. (Admittedly, there are other methods of performing all these functions, but the Dock is arguably the easiest.)

Similarly, the Trash icon is only to be found in the Dock. You can of course send files and folder to the Trash with a key command, but the only way of dragging a file to the Trash is onto the Dock. Clicking on the Trash icon is the easiest way of opening the Trash to recover trashed files. You could not drag a file from a Finder window into the Trash within LaunchPad.

There is always a compromise to be struck between "ways I'd like to do things" and "ways that the OS is designed to do things". Sometimes it's possible and desirable to modify the defaults; and sometimes it's not possible (without making significant alterations that may cause unforeseen difficulties, limitations or even 'damage' to the OS).

Customisations to Apple's System files are possible, but require regular maintenance to ensure that new system updates have not restored Apple's original data, or changed things so that the customisation no longer works or even causes problems.