Is it permissible for a person who hasn`t made ablution to call for prayer (Adhan)?
All perfect praise be to Allah, The Lord of The Worlds. It is disliked for a person with a minor impurity to call for prayer, but if he does , then it`s valid and sufficient. And Allah Knows Best.
Is it permissible to slaughter one animal as a sacrifice and an Aqeeqah (the sheep slaughtered on the seventh day from the child`s birth)?
It is impermissible to do so since each of them is slaughtered for a different reason.
Has Islam made it incumbent on us to give our children particular names?
No, it hasn`t, but it is desirable that we give them good names.
Is it permissible for the person who wants to travel from the United Arab Emirates to Jordan during the daytime in Ramadan to break his fast before leaving his country; knowing that he had embarked on journey half an hour after dawn?
Praise be to Allah the Lord of the Worlds.
The person who made the intention to embark on journey after dawn must observe fast for that day, because it became an obligation on him before engaging on journey. However, if he experienced unbearable hardship while on travel, then he is permitted to break his fast, but he must make up for the missed day. And Allah The Almighty Knows Best.