You can do Metta(loving kindness) meditation. But if you are looking for something to chant, you can chant the Karaniya Metta Sutta. Focusing on mindfulness is very good but that is not the only meditation taught in Buddhism. If you are doing Samatha(tranquility) meditation, there are about 40 types of them. If you feel afraid, you can chant the nine virtues of the Buddha. If you see many nightmares at night, you can chant it before you go to sleep. It does work. If you are into Satipatthana(mindfulness) meditation, there are four protective meditations you can do to help that.Buddhists do not pray to gods and ask for things. But if you are asking for something you can do spiritually to help someone sick to recover or a dead relative to go to a better place etc., you can do good deeds and dedicate the merits to that person. You can also do good deeds and wish for a certain outcomes. Ex: Once there was a girl who offered flowers to Ruwanwelisaya(the stupa with the largest collection of relics of the Buddha) and wished to be beautiful. It didn't end well for her even though she got what she wished for. So wishing for material things is not recommended.
If you want to pray, you can do it just like meditation. Use a "mantra" as an object of meditation, you do not need to ask anyone for this. Yes, you can pray for the benefit of everyone, this will generate good karma because our intention generates karma.