When you download a file and choose to open this file in an external application then Firefox saves the file to the OS temp folder. Files stored in this location can be removed at any time, so there is high risk that you lose edits made to this file and thus the file is saved as read-only. You need to use "Save as" in the application and save the modified file in another folder to make sure you do not lose your edits.

Are you saying there is no way to open the file from sharepoint and clicking 'Check Out'? Is there any way to have firefox use a different folder(other than OS temp) if that is what preventing the checkout?

You shouldn't have a problem to open this file in Sharepoint. This is merely about making edits and saving the file in the same location instead of using "Save as".

So is there any settings change I should make to have the checkout/checkin(currently it is read only everytime I open even it is Checked out) option from Sharepoint and make the change without saving(Save As) the file manually in a different location?