Yes, you can connect. Make a taper waveguide transition from circular waveguide to rectangular waveguide.

yes, you need transition as mentioned above. I would like to suggest you to consider the effect of soldering in your simulation. During simulation, do not use waveport at the end of your transition (for verification purpose). If needed, use coaxial probe at proper place and define waveport at the end of coaxial probe.

Yes, you need a commercial transition from circular to rectangular waveguide

You can also mill and turn a transition,  Mill a rectangular waveguide through a block - you can get away with a reasonable radius in the corners and still get a good vswr connecting to proper waveguide - then centre it in a lathe and turn out the cone you want.  This is probably best for horns with up to 30 degrees taper, but try modelling it - the intersecting cone and rectangle are quick and simple to model, and it may work well with wider tapers.