All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
It seems that there is no religious impediment to calling a child 'my little angel'. This does not involve a violation of the sharee'ah, though it is better to avoid doing that because some scholars deemed it disliked to name a child 'angel'. Shaykh Ibn ʻUthaymeen advised in one of his monthly interviews, "I dislike for the Muslim to name his daughter Malaak, (meaning angel). Has he run out of names? There is an endless amount of names that he could have opted for instead of this one..." However, on a different occasion, he said that the basic principle in this regard is that it is permissible to use such a name. He said, "Some use the names 'Malak' or 'Malaak' or 'Abraar' and the like. What resembles the names that the Prophet forbade must be forbidden and changed. However, the basic principle in choosing names is permissibility because the rule that every seeker of knowledge should understand is that the default ruling in other than acts of worship is permissibility; whether customs and habits, benefits or other unless there is proof of impermissibility..." [Liqaa' Al-Baab Al-Maftooh Series]
Regarding traveling without a male mahram (permanently unmarriageable kin); it is prohibited. It is prohibited for the Muslim woman to travel unaccompanied by a husband or any of her male mahrams except due to a strong necessity or need, regardless of the length of the journey. Please refer to fataawa 83795 and 262621 about the evidence on the prohibition of a woman's travel without a mahram.
Allaah knows best.