Salaam & Greeting

Greeting with salaam alaikum

Q: Is it ok to just say سلام عليكم? In Hayaatus Sahaabah (Part 2), under chapter 9 -

خروج الصحابة رضي الله عنهم من الشهوات - :التسليم على المسلم - عمل ابي امامة رضي الله عنه في ذالك

A riwaayah comes wherein Abu Umaamah رضي الله عنه said this.

Greeting a non-Muslim helper

Q: My nani is bedridden. She has a female Christian attendant who comes everyday in the morning and leaves at night. She wanted to know if she can say salam to her when she comes in the morning. If not, then how should she greet her when she comes? Not saying anything appears rude and cold.