strange feline behavior

Question
I took in a stray cat about 2 months ago.  We tried unsuccessfully to find her real home and decided to keep her as it was winter and extremely cold.  She is a beautiful cat and not much trouble for the most part with these exceptions that I have no idea how to address:

1)  She is constantly meowing - loudly - and tries to get outside every time we open the door.  She is declawed and is not neutered so I don't want her outside.

2)  She wakes our entire house up every day at 6:00 am with her very loud, obnoxious meowing.  She paces up and down our hallways until she wakes us all up.

3)  As of late, she has stopped using the litter box and I have found the evidence of this in just one particular corner of our den.  I'm not sure if it's just feces or if it's also urine.  I have moved the litter box to this particular area to see if this helps the problem.

4)  She likes being around my children and they love her.  They are boys and can be very rambunctious and loud.  Nothing seems to bother her except when they are crying and then she literally attacks them and tries to bite them.  She could easily break the skin with her teeth, but it almost seems like a warning.

I am at the point that it seems time to remove her from our home but I don't want to do that until I have investigated every option and given us all every opportunity to correct the situation.

Any suggestions?  Please help.  Thank you.

Answer
It sounds like heat behavior and getting her spayed should minimize most of the behaviors especially the meowing and not using the litter box.  

Make sure the litter box is scooped every day and in a quiet location...also try CAT ATTRACT LITTER and consider using FELIWAY.