haribol prabhuji pamho., agtsp., agtsg&g.,
regarding sacred threads it is nice if one can offer anew sacred thread every ekadasi
For Saligrams I have a 18crt gold thread that my Pradhan sila wears, and another couple have 9crt gold threads, they never need changing. In Narasimha purana it is mentioned that if one offers gold brahmin thread with red silk thread it is the most perfect brahmin thread and never needs changing, that is cited somewhere in 11th canto Srimad Bhagavatam. Wearing these threads yes the Deity/Sila can wear them while bathing. I wouldn't bathe Them wearing a cotton thread, I remove the thread from the Deity and then after sprinkling with water re-offer it when replacing idam upavitram "mula mantra" upavitram samarpayami
Regarding sacred threads maha-prasadam no it cannot be warn by us, it is best buried under a Tulasi plant, or make a hole and plant a Tulasi plant upon it same thing.
I hope that helps ys, JTCd