بسم الله الرحمن الرحيم
Khalilullah means Allah’s friend. It was the surname of Hadhrat Ibrahim (may Allah have mercy upon him) and Kalimullah means the one who talks Allah, it was the surname of Hadhrat Musa (may Allah have mercy upon him), both the names are correct. You may choose any one for your bhatija.
(2) It should be noted that according to Islamic teaching it is important that the name has suitable meaning. It is not important to look the date and month the child was born as it is the practice of others.
Allah knows Best!
Darul Uloom Deoband