I live just to the West of Phoenix Arizona where it is very dry and very hot in the Summer and I am trying to figure out if my Palm Trees are Mexican Fan Palms or California Palms ??? Also I am trying to figure out how much I should be watering them ???
Palms are very difficult to distinguish, but the shape of the trunk paired with the leaf arrangement leads me to believe that it is Washingtonia robusta or the Mexican Fan Palm.
Here is an article that will help:
https://www.gardeningknowhow.com/houseplants/fan-palm/growing-mexican-fan-palms.htm
Pot is not very large (about 3ft. high and 2 feet across). Palm tree is about 3 feet high (from bottom of stem to highest fan peddle) and still getting new growth (recently). My question is how long can it stay in this size pot and continue to grow before it needs to be planted in the ground or put in larger pot? When is it needed to be transferred to continue growing, how I you tell when it is time?
You will not have to transplant until you see roots on top of the soil, or coming out of the drainage holes.
Here is an article to help you care for the Palm:
https://www.gardeningknowhow.com/houseplants/fan-palm/growing-mediterranean-fan-palms.htm
My fan palm is producing new leaves but they are all seem to be crammed up at the crown and not growing
This is likely for the same reason as your Cordyline. Make sure to test pH and nutrient contents, as well as letting your soil dry out, thoroughly, down to about 2 or 3 inches between watering. Please consult the links provided in your previous question's answer.
I own what I believe to be an European Fan Palm, a side sucker shoot broke off and it has zero roots on it, my question is how can I get it to root, so I later can plant it in a pot with dirt? Do I try and root it in water, or can it go straight into a pot with soil?
I did some research on this and the consensus was they grow faster from seed. It is very time consuming to try to get a sucker to root, but it can be done, although it may take a couple of years. Insert the tip in rooting hormone with a fungicide and plant in gritty soil in a large pot. Here is the endeavor by a palm society member:
http://www.palmsociety.org/members/english/chamaerops/031/031-14.shtml