Is it possible to estimate vegetation ( crops) height using free of charge satellites, like sentinel or Landsat, with QGIS?
Estimating vegetation height is a complex thing to do and potential methods depends on the required accuracy.
If you are only looking at one crop type, in one specific region, you can get away with creating a statistical relationship between optical data (such as Sentinel-2), radar data (such as Sentinel-1), and the crop height (from field measurements). This will give you a model that will provide reasonably good results, for that single crop type, however, it would not be transferable to other crop types. I have seen this done for forests canopy height and the same approach should also be usable for crops.
The problem arises when you want to do to across a myriad of different field types, where you'll have to create a tiered approach, where you first determine what is on the field, and then apply the appropriate model to that area. All-in-all, not an easy task, but by no means impossible. However, do expect significant uncertainties in your results.
Another difficulty may be to get accurate training data, which is why I suggest field data.