Difference between Ein weiterer , Anderes and Zutsaliche?
andere/s/r means other in the sense of different, not additional. Zusätzlich is additional when you keep what you had before... For example you wouldn't translate "We have to try another time" (= one more time) as "Wir müssen es ein zusätzliches Mal versuchen", but "... ein weiteres Mal". If you say ".... ein anderes Mal versuchen", you mean "try another time" like "try a different time", even if you did not try this time ;-).
Hallo Foopiboi! This one is a classic :)
To my understanding, "andere" would be "other"; "weitere", "one more", and "zusätzlich" (if you cannot write the Umlaut, you may write "zusaetzlich", but be aware you have to take it into account, as it changes the pronunciation) "additional". This is a very simplified view, please check in any good dictionnary, for exemple the Pons
The different endings refer to the gender and number of the following noun, and/or the case of the phrase. "Ein weiterer" would call a masculine noun in singular nominative; "ein anderes" a neuter noun in either nominative or accusative singular; "eine zusätzliche" a feminine one in nominative or accusative singular. "Einen weiteren", "einen zusätzlichen", "einen anderen" would call for accusative singular masculine. "Weiteren", "anderen", "zusätzlichen" (no article) would be dative plural (all gender). "Einer weiteren" and so on, feminine dative singular, "einem anderen" masculine or neuter dative singular, and I will let you discover the delights of genitive ;)
Theses tables you may find useful. Don't let yourself be discouraged: everyone has to struggle with them at a moment or another, but it always work out in the end with a bit of dedication.