This guide only covers EN -> JP autotranslate. Feel free to add your own (I am completely unfamiliar with DE/FR).
I think this guide will be useful to you if you play on a JP cluster or server. I play on a cluster/server where 99.9% of duty finders are JP, so I'm not up to date on how EN players use autotranslate.
For anyone fluent in Japanese, please correct me if I am wrong as English is my main language.
Potential pitfalls
Without knowing what appears on the other side, what you say could make no sense, rude, or plainly wrong.
{Let's do it!} -> {よろしくお願いします!}
The Japanese phrase that comes out has no equivalent in English. Why is it in autotranslate? It is the most commonly used phrase by Japanese people, so it is extremely useful, but because it can't be translated, this phrase is the number one potential pitfall.
"Let's do it!" is not even close to what it actually means, but it is always used by JP players when joining a party so as long as you use it that way then it is correct. Do not use this during a dungeon (e.g. after taking a break) - it won't make sense. Google yoroshiku if you want to know more.
{Good game!} -> {お疲れ様でした。}
Commonly used by the EN community in various multiplayer games, the Japanese counterpart meaning is not even close.
This phrase means something like "You did good work" and is usually said after a day of school/work/sports. Again, it is always used by JP players when a party ends so as long as you use it that way then it is correct. Anytime you try to use {Good game!} for its meaning, it will be wrong.
Those two are the most important ones IMO, and will last you a long way.
However if you wish to keep reading...
Minor annoyances
{Nice to meet you.} -> {はじめまして。}
Can be used as a general greeting when meeting a person for the first time. It literally means "First" in Japanese so if you use it with a person you have met before, they may think you are forgetful or rude. Do not try to use this in past tense (i.e. It was nice to have met you), it does not work.
{Japanese} -> {日本語}
The Japanese counterpart refers explicitly to the Japanese language so something like "He is {Japanese}" is wrong ("He speaks {Japanese} is correct).
{Hello!} -> {こんにちは。}
This translates to "Good afternoon." or "Good day."
Doesn't work well in the morning or at night.
{That's too bad.} -> {残念です。}
Correctly translated, but the sarcastic tone does not carry over if you intend to use it that way (literally: that's regretful).
{You're welcome.} -> {どういたしまして。}
Correctly translated, but Japanese people very rarely use this (google if interested). Use: {Don't worry about it} -> {気にしないでください。}
{Take care.} -> {気を付けてください。 }
This translates to "Please be careful" and not a farewell.