I underwent Samashrayanam and Bharanyasam from Shrimad Azhagiyasingar in 2017. Since then, I have been chanting the shlokas, Ashtaksharam, Dvayam, and Charama Shlokas from the book provided at that time, along with Sriyai, daily in the presence of the Lord after morning Sandhyavandanam as Nityanusandhanam. Can these be chanted every day? What other mantras or shlokas can be chanted along with these?

Every day, along with Sandhyavandanam, all these mantras should be performed as Japa. It is good to sit down, perform Sankalpam with Pranayama, and do them as Japa. It is better to do it as Japa rather than just reciting it as Nityanusandhanam. Sometimes, they are recited during archana at the time of Tiruvaradhanam. Whatever mantras you know, you can recite them all. If you do not know the mantras, you can recite shlokas.