My name is ***** ***** I will be the licensed immigration attorney helping you today.
As far as getting married, yes she can come to the US and marry you and then leave. You can also marry in any other country. As long as the marriage is legal in the country that you get married then it will be valid in the US.
If she comes here and you get married and then she leaves to Belgium temporarily, yes she can still begin the process to petition your permanent residence in the US. However, the permanent resident is two parts. And for the second part, she will have to move and be living in the US. This is because she is supposed to be living in the US in order to petition her spouse to live in the US and you are supposed to be living together also. She cannot be living in Belgium while you are living in the US at the end of the process.
Good luck to you during this process and I hope this answer has helped you!
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