I have never done that, in theory as long as you have the software and its configuration it should work anywhere. (Have a look at docker, it might be better if you want to have a portable setup).
You only need to have your config file + data, and you could deploy Cells anywhere as long as you have docker installed and network access (otherwise you should save the image locally) to run containers.
Yes, you can make use of your internal hard drive on your laptop.
For that you must edit the datasource and select another folder (in your case point to your hard drive)
You could automate the installation with a yaml file, here is how we do it on docker, the principle is also the same without docker?
You could script a regular installation by running ./cells install --yaml install.yml.
You can use a tool such as to have a tunnel
this will allow you to have access to your laptop from the outside, have a look at their documentation.