Yes and no. One of the great convenience features of ArcGIS (both Pro and Desktop) is that they "project-on-the-fly", meaning that they perform automatic real-time reprojection of your data. Once a projection is assigned to the dataframe (either by adding the first data layer or by manually setting a projection), any subsequent layer that is added is displayed in that projection. In that sense, the answer to your question is yes. There are a couple of important caveats, because the real-time projection is not perfect. In some cases, the layers won't line up exactly on the screen. I think this usually happens when the layers are not just in a different projection, but also have a different datum. You will usually only notice this if the two layers have common features, and you zoom in very close (the error will typically be sub-meter). Because of these minor discrepancies, there are a few best practices:

1) Never edit a layer that is in a different projection than the dataframe (you should get a warning if you try to do this)

2) Never use layers that are in different projections as clip features (or similar editing and geoprocessing tasks) for each other

3) Don't rely on spatial calculations (e.g. area) on layers that aren't in the current projection

4) By the same logic as #3, ArcGIS will let you take measurements and do calculations on unprojected data (GCS coordinate system), but these will almost always have substantial errors. This is true even if the dataframe is set to a GCS coordinate system as the "projection".

I suspect so because ESRI constantly upgrading their software; however, except if confirmed by getting in touch with ESRI in Redlands California USA, your final maps will be incorrect

As same as Desktop: project on the fly