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Sorry, but my spam killer killed several messages and I couldn't
retreive your addresses.....so to answer your questions about the carrot
cake recipe
1. yes, there are no eggs
2. bake at 300 degrees in a well greased pan.  Even better, line pan
with parchment paper
3. you can use any size pan, it'll bake in about 35 min for a 9"
pan...test for doneness.  For my daughter's Christening cake, I used a
wedding cake set with a bottom layer 18" wide and the top layer 7" wide.

a further tip..and trick.  I took a course in professional baking before
the christening and got this tip.  The reason that a cake bakes up
uneven is that the pan itself heats up first and bakes the outside way
before the inside [center ] is done.  To counter that, take an old
flannel nightgown or sheet and cut it 3x as wide as the pan is deep and
long enough to completely surround the pan.   Now, here's the trick.
WET THE FLANNEL, WRING IT OUT , FOLD IT IN THIRDS, WRAP IT AROUND THE
PAN AND SECURE WITH STRAIGHT PINS.   Then, grease pans and pour in
batter and bake.  The flannel will keep the pan cool and will not
burn.   The chef who taught the class said that they would also use wet
newspapers in a pinch.

You can purchase strips covered with teflon to cool pans, but I find the
flannel strips work better.

The cake bakes perfectly flat with no need for triming.

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