Some orchids will bloom again from the old stem but most experienced growers cut the stem off once the blooms are spent....sure you might get a side branching spike but the number of blooms will be less.

Yes, you can divide the plant if you wish and you will end up with two plants but usually you would wait till the plant had a few more pseudobulbs before doing the dividing thing. Two smaller plants need smaller, appropriate sized pots for your potting material and conditions and should you use the old spag? buy some new spag or use some other potting material? Cannot advise here because i do not know what your growing conditions are like in zone 8 USA.

It looks like a hybrid oncidium type so I would cut the spike right back as they seldom throw a secondary spike from the original.

I would leave it as one plant in a single pot and remove as much as the old moss as possible without damaging the roots.

Thank you very much. I whacked off the bloomstalk, but while I was trying to get all the moss out of the roots, the plant fell into two parts. I looked but did not see where it had ever been connected. Also, one of the two pieces had bark in its roots, and the other had none, as if they had been potted seperately at one time. I couldn't get all the old moss out without tearing up roots so I got as much as I could and quit.

I am grateful to both of you for the information.

John

sometimes growers will put two smaller plants into one pot so they look bigger and they can charge more.

Repot both halves into the smallest pots you can. Orchids not only like tight shoes, but if there's too much medium and not enough roots, the medium can stay too wet and gradually rot.