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Yes, plants in clay pots do tend to dry out more quickly and need watering more often. You can still be successful with a clay pot though. You could try increasing the humidity in the air around the orchid. Orchids are also sensitive to water quality since many species don't grow in soil and are adapted to relying on pure rainwater and mist in the air.

Here is some more information on watering orchids:

https://www.gardeningknowhow.com/ornamental/flowers/orchids/indoor-orchid-care.htm

http://www.uvm.edu/pss/ppp/articles/orchidgrow.html

Inspect your Orchid for any signs of pests or disease.
Yellowing leaves can also be due to watering issues.
Pruning can be done after your Orchid is done blooming and your plant will need a dormancy period. Make sure you use clean, sterile tools while working with your Orchid.
Here are some links with more information.

https://www.gardeningknowhow.com/ornamental/flowers/orchids/common-orchid-problems.htm
https://www.gardeningknowhow.com/ornamental/flowers/orchids/how-to-prune-an-orchid.htm

hi, if you live in an area that is warm ...and is not going to freeze...put your orchid outside..where there is good light but not in direct sun...hang it in a tree..or from the eve of your house....mist your orchid once a week with water that is not city water but distilled.....it will grow roots outside the pot..this is natural..hope this helps.....take care barb

This could be black rot; see the following articles for information. The disease is contagious so separate it carefully from any other orchids you have.

http://edis.ifas.ufl.edu/pp260
http://ipm.ucanr.edu/PMG/r280111011.html?printpage

It sounds like you have keikis, or baby orchids! Yes, you can remove these (it's best to let them develop a bit before removal) and grow them separately. Here's how:

https://www.gardeningknowhow.com/ornamental/flowers/orchids/orchid-keiki-care.htm

Unfortunately, this can be a sign of a disease or insect damage. If the patches are large, it could be either a fungal disease or a bacterial brown rot caused by a species of Erwinia bacteria. If the patches are tiny, it could be an infestation of thrips or another small insect.

Check whether you see any small insects on the leaves. To remove insects, try wiping down the leaves with a mixture of rubbing alcohol plus a tiny bit of dish soap.