Can I dry hop and cold crash in primary?

I have recently read posts where people do not use a secondary much anymore. With this in mind, is it practical to dry hop and cold crash in the primary, as long as the total time is not more than 4 or 5 weeks?

Yes.

Unless you want to save the yeast for another brew. Then you want to transfer it to another vessel before dry hopping.

+1. That was going to be my exact response.

Keep in mind you will be dry hopping 5-10% more volume and the yeast absorb the hops better than the wort. If you want comparable results to dry hopping in secondary use more hops.

My cold crashing will consist of placing the primary in a large tub of water, which is in my 62* basement, and dumping ice in it as needed. Since I dont want to drop too much yeast to not be able to carb my bottles, how long should I risk my “ice bath” cold crash? Its an extract Dead Ringer that will have been in the primay about 26 days prior to cold crashing.

Once you get it cold, a couple days is usually good enough to drop most of the sediment and should leave behind plenty of yeast to carbonate.