Are the constellations in the northern hemisphere ever visible in the southern hemisphere?

Yes Orion is clearly visible in the January sky. If you would like to learn more check out this free course. Https://www.futurelearn.com/courses/orio... BTW Jupiter (today) is just above and to the right of the Moon.

I'm not sure what you mean by "shining star at the bottom". As seen from the northern hemisphere, the bottom right bright star of Orion is called Rigel. If you follow the belt of Orion towards the horizon you should see Sirius which is also bright and below Orion.

Yes. 8 of the 20 first magnitude stars are in that region in - Rigel & Betelgeuse in Orion forming a diagonal & around - Sirius (the brightests) & Aldebaran as extensions of the other diagonal; Capella, Aldebaran, Pollux, Procyon. If you are lucky to be in the tropics (like me) you can see Achernar & Canopus, the second brightest star beyond.

December - January shows the most dazzling part of the sky.

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