Glenford, welcome to the board! Please check out the long thread linked by fishmom above, "The Phal Abuse Stops Here." You will learn a lot.
The main thing, as already mentioned, is that watering with ice cubes is not ideal -- far from it. Your orchid has survived okay so far, but if you want to keep it around and give it an opportunity to rebloom for you many times, there are better ways to water. Either soaking or drenching are the ways most of us do it.
Also, if the glass container your orchid is in has no drainage holes whatsoever, that is a problem, especially when you start to use water instead of ice cubes. You don't ever want the media (potting material) to be wet with no air flow, no way to dry out after watering. Some of us use plastic pots, some prefer clay or ceramic or maybe something else, but all orchid pots must have good drainage and air flow.
As far as the old flower spikes, you can go ahead and carefully cut them off if they have turned totally brown. If they are still green, the plant may still be using some of the nutrients to be gotten from it, or it may even rebloom from the same spike.
There's more to it, but this board is a good place to get started. I would also encourage you to check out the American Orchid Society's website:
The American Orchid Society
Look under "All About Orchids," then go to the "Culture Sheets," and then click on the ones for Phalaenopsis. If you need any help navigating their site, just ask, and I'll give you more specific links.