All user files and settings are stored in /home/<user>.
If you already have a dedicated partition for /home, you may only override Mint’s system partition with Manjaro, and reuse the existing home partition (manual partitioning may be necessary): [HowTo] Use multiple partitions / drives in your Manjaro installation
If you do not have such dedicated partition, you need to backup those files first – configuration files and folders are usually hidden! – as they will be lost during Manjaro’s installation (the system partition is always formatted).
Manjaro should be ahead of Mint regarding application versions. If you kept your configuration files, the first start of those applications on Manjaro should update them to be compatible with the newer versions. Though this also means that, once done, they would not be compatible with Mint’s versions afterwards.