SNAP doesn’t support atmospheric correction.
Noise cannot be removed, only coarsely approximated subtracted from the phase. This is only possible with large stacks of images, for example by estimating the atmospheric phase screen (APS, short explanation here). This technique is not really suitable for common interferometry, but rather for persistent scatterer techniquest to derive surface deformations.
Values of high coherence tell you where your data is suitable. Please have a look at this post: Some explanations about concepts of fringes of interferogram and coherence - #2 by ABraun
Besides that, ESA provides nice explanations on interferometry: ESA - InSAR Principles: Guidelines for SAR Interferometry Processing and Interpretation<br>(ESA TM-19)
Here you will find three documents:
Part A is for readers with a good knowledge of optical and microwave remote sensing, to acquaint them with interferometric SAR image processing and interpretation.
Part B provides a practical approach and the technical background for beginners with InSAR processing.
Part C contains a more mathematical approach, for a deeper understanding of the interferometric process. It includes themes such as super resolution and ERS/Envisat interferometry.