Have tried burning jpeg photos to CD-R & DVD-R using windows photo gallery, pictures file & straight from SD card none of these work in other computers or my compatible DVD player do I need another program to burn my photos from or do I need to finalize my discs and how do I do this.

Try copy the files to your hard drive first and then burn to disc

Here is a link with some free burning software
When you want to burn photos to discs, use Burn Data CD/DVD

Free CD and DVD Burners, Mastering and Copying Programs
Free CD and DVD Burning (Writing) and Copying Software (thefreecountry.com)