I am using Ubuntu 20.04 on an old machine. It has taken me 4 days, with multiple CPU freezes along the way, to finally download the full NXT blockchain.
I am terrified of making a mistake and losing all of the blockchain data I have downloaded and having to start again from the beginning.
So before I do anything further I would just like to know:
Can I simply close the Terminal, and turn off the computer?
Then , when I turn on the computer, reopen the terminal, and run the NXT client (./run.sh), and then login via the http://localhost:7876 web browser... Will the entire blockchain still be saved?
Or, do I need to do something special, or enter some command line into the Terminal to save the blockchain before I close the Terminal?
I would recommend shutting down the node and waiting for a complete shutdown before shutting down the computer. If you just run the node using ./run.sh from a console you can try to focus the terminal window and press CTRL-C to send a quit signal to the process. You should see how the node initiates the shutdown sequence. When the node shuts down it compacts the blockchain database so it might take a while, even some minutes on older computers.
Eventually it will return to the command prompt. You can now safely shut down your computer.
Once you start your computer again you would start the node and the blockchain database will resume synchronization from the point it was when you shut it down.
You could also make a copy of the nxt db you have downloaded for the future, as then any new installations will only have to download from today (or the date copy is made) by using the copy of your db.