First notebook entry: Introducing myself

I would want to (be able to) speak and understand English so that I would can traveling and learning study abroad.

"would" in the way you used it and does not fit in the context. "would" is an adverb phrase and a commenting function, structure example: "I would do ____, but ______" or "I would like ______ if _______". If you want to use "would" you can say "I would want to speak and understand English if I could travel and study abroad" the key is the preposition "IF"

"so that" - shows that it leads to certain results; you actually do not need "that" here, but it makes sense in this sentence as well as not in the sentence.

"study abroad" sounds better than "learn abroad"

Good luck with your English studies! I hope you can travel and learn a lot in the future!