I have downloaded the Ubuntu 13.10 iso several weeks ago, but hadn't got a time to install the OS, so should it be okay if I burn the ISO to my USB using that ISO, or I should redownload? Will there any new updates being rolled onto me, or they will be updated straight at install? Thanks. Sorry for my bad english.
You can use that ISO.
After installation you will be prompted to update the system and this update will be a bit longer than usual (since it will update everything that was changed since you downloaded it).