To address your points
- If you have the chance, try to get Level 1.1 data, apply radiometric calibration and Range Doppler Terrain Correction where you can select the coordinate reference system.
- If you don’t get L1.1 data you can apply the mosaic operator (described here) to geocode your product (terrain effects will not be eliminated) and re-project it to UTM.
- SNAP cannot correctly display two products of different pixel size side by side. They show the same area and during stacking they will be resampled to a the resolution of the master. This is just a visual thing at the moment, you can proceed.