But can I instead do a direct translation so the sound is the same in both languages? That is, "Ga" in Chinese (pinyin) directly? How, then, do I create a character or word corresponding to the Pinyin sound?
No, you cannot. Words and characters can be invented, but it will take time for people to broadly use them and include them into their vocabulary. And only then are they absorbed into the language. If no one accept your invention, then it's meaningless.
Say we have some new words in Germany that have never been translated.
Ga = To walk upside down
Ba = Half unicorn half flamingo
Ti = To fly underneath a bridge
How would we go about translating these into English? I can, of course, find the corresponding terms in English and string them together. Like [WALK][DOWN] or [UNICORN][FLAMINGO], etc. But can I instead do a direct translation so the sound is the same in both languages? That is, "Gah" in English directly? How, then, do I create a word?
I think it's quite obvious now. You didn't translate it, you just invented a new thing somehow following the rules in that language. But it means nothing, no one, except those who have read your works, will understand it. Of course, if you just intend to get it across merely to your target readers (Even in this case you should explain its meaning for once), you are fine to go. Or if your masterpiece is so popular and famous that everyone feels shame if he hasn't read it, for example, 鲁迅 just coined a character 猹 (it is non-exiatent before) referring to a kind of animals local to his hometown, and it's nothing other than pronounced as what the villagers call that animal. But today everyone knows it and accepts it as part of our language, so it's included in unicode encoding. That is a great example to your question.