lizard mating

Question
Hi, i live FL where a whole bunch of brown anole lizards live and recently i caught 3 of them. Two are males and 1 is a a female. So I left them all in 1 cage for 10 minutes and when i came back  the female was on top of one of the males both laying on their backs and shaking! Their eyes where open and both were breathing but i do not know what they were doing. Should i catch 2 more females to make the first female feel less stressed out? Is it usual for them to mate on their backs? What should i do if the male lizards get territorial and fight? How do I get 1 male and female to mate?  
Should i put only them two in a cage together or separate them? Will the lizards eat their eggs? How do i know if their pregnant or not? Thank you for spending time to respond to my questions.
With graditude, 6th grader Sara

Answer
"Normal" mating would involve the male grasping the female by the neck and remaining on top-though sometimes they do fall over...  Not sure what you saw (would have liked to have seen myself!).  

As to stress and pairing-more space=less stress.  With active lizards like anoles figure 10 gallons per lizard IF your cage is not more than 16 inches tall!  In other words a normal 55 gallon tank would only house 2-3 lizards because so much of the space is wasted on height.  One male w/ multiple female is the best way to go.  

Sometimes they will eat each others eggs but you can avoid this by covering the eggs with some small piece of plastic like a pill bottle lid or a small paper water cup.  You will be able to see the swelling of the female's abdomen if she gets pregnant.  If you live in FL and you set up the cage properly allowing them to cycle with the seasons they should mate w/o you doing anything more than normal feeding and care.  

FEED you prey items before you feed your lizards-the most important step that is most often missed.  Buy your crickets smaller than you need them and grow them to the proper size using good quality foods.