BJ, welcome to our forum, you have already found it a place to ask questions and you have some good ones. I am going to try to answer a couple of your questions. No doubt you will get many more responses, but here goes.
<was reading in a beekeeping book that said we should mash the queen then rub her mashed up goo all over the hive so the others smell her death and make another queen real fast. But I have to admit I just wont be able to do it or so I feel at this time.
The idea of mashing up the queen so others smell her death and make another queen is something that I have never heard of. I wonder where you read that.
<I know it may seem silly to some but the thought of doing that to what will be my bees that I will be tending to seems cruel. And the thought of putting them in alcohol also seems cruel, does that burn them or make them suffer?
The bees die instantly in alcohol, they don't have time to burn or suffer, it is a way of quick kill and preserving, as with the queen, if she needs to be killed
<I dont mean to degrade the way ppl put down their queens but at this time in my niave early stage of learning about beekeeping Im thinking it seems cruel. I know I have much to learn yet.
When I first began keeping bees, I thought it was cruel to kill a queen. I still find it hard (I have only killed 2 queens in my experience and it was a tough thing to do, but, though love, the life of the entire colony meant more to me than one life of a queen). But look at it this way, if it means that the entire colony would die because of a poor queen, what then would be your choice? Sometimes we must make harsh decisions. Usually if the queen is not very good, the bees will see to that death anyways. They will perform supercedure where they raise a new queen and she is killed.
<What if a queen is left to be old and die on her own what will happen?
If this happened, the colony would recognize her death (lack of the queen pheromone that is distributed all over the colony of bees quickly) and begin to raise a new queen immediately, within the hour of the lack of the queen pheromone that was present when she was alive within the colony
<What would happen if an old queen bee was taken from the hive and driven far away and let go to fly would she make a new hive ?
This queen would die. She cannot feed herself, every need of the queen is taken care of by the house bees. If she was taken away while she was still laying eggs, her ability to fly would be greatly diminished and she probably wouldn't fly anywhere anyway.
<would my bees fly off far away and find her ?
If the queen was removed, your bees would immediately begin to raise a new queen, providing there were larvae in the hive to feed to prepare the larvae to become a queen (who is fed only royal jelly, as opposed to worker larvae that are fed a combination of royal jelly, pollen/honey). This kind of thinking that the bees may miss her and look for her is a human emotion, not honeybee, we can't equate those
<would she just fly around lost until something kills her?
Yes, if she could fly, but likely not flying very well
<would she find her way back home and cause trouble with the new queen and divide up the hive?
She would never, ever find her way back home, period.
I hope these answers may clear up some of your questions, help you a little bit, there is so much to learn, lean on us to help you, answer your questions, and there will be many, enjoy your time year. Best of a beautiful and wonderful day, Cindi