Marhaba !

- good schools that follow UK curriculum which also offer Islamic studies

www.iscdoha-sabis.net
www.qis.org
www.qataracademy.edu.qa
www.newton.com.qa
www.dess.org/

- childrens madressas (like in the UK) which can offer Islamic studies of Quran and Kitaabs
Even I dont know, if you get this info do share with me too

- living in Doha. Which is the most suitable compounds.
QF(Qatar Foundation) but Apartments @Ramadah, Al-Sadd You will find shops, Hospitals etc.. etc.. very close so I think this is best