[And when I get the new computer, and it does not have Microsoft Word, I just go online, download this Open Office software, install it on my computer, and then I plug in the Flash Drive, select the My Documents option and a thing will pop up asking me where I want to put it AND I'LL SEE OPEN OFFICE and I'll select it?? Did I get this right?]

All you would need to do before or after installing open office - is just copy the documents file over to the new computer in the My documents folder
Just like the same place it was on the old computer, only it will be on the new one & the copy still on the flash drive.

When you start Open Office, or even Word Pad - you might test Word Pad now before you do any changes - open a doc with word pad -I haven't tried it . I don't have any word docs to test it with.
It did open another file type.

When you start Open Office - then in the menu bar select Open and it will pop up a box where you can find the file or document that you want to open.
but you may not even need it if Word Pad does the job.