AsSalam Aleykum Werahmetulahi Weberekathu Our dear and beloved ustadh. May Allah preserve you and your family, grant you the highest level of Jannah . Q1) is it permissible to check upon non Mahram cousins and their mom through text ,they are not Muslims and my dad heavily insists that I do so .

Ustadh AbdulAziz al-Haqqan

Check on them through their parents for example, and you can give salam unless there is fitnah to be feared then you do not obey.