If the imam does not leave time for reciting Surah Al-Fatihah, is the recitation of Al-Fatihah waived for the follower?
The recitation of Al-Fatihah is not waived for the follower. They should recite it silently, even if it causes a slight delay in following the imam in bowing (Ruku'). And Allah Knows Best.
Is wearing a cap permissible for boys, or girls?
All Perfect Praise is due to Allah, The Lord of The Worlds.
In principle, anything is permissible sol long as there is no Sharia evidence prohibiting it, thus wearing the cap by boys is permissible as long as it isn`t done in imitation of the disbelievers. Moreover, a Muslim woman should avoid all that which attracts the attention of men because whatever leads to the forbidden is forbidden. And Allah Knows Best.
Is the prayer of someone who didn`t face Quibla (Ka`ba direction) valid?
All perfect praise be to Allah,The Lord of The Worlds. Facing the Quibla is a condition for the validity of prayer, and the prayer of the person who hadn`t faced the direction of the Quibla is invalid, and he is obliged to repeat it. And Allah Knows Best.
What should one who doubts the validity of his ablution and performs it frequently do?
Whoever doubts the validity of his ablution after finishing it, his ablution is valid. This is because the default is the validity of the ablution, and because doubt after finishing an act of worship doesn`t affect its validity. And Allah the Almighty knows best.