Oof that aint easy. Good luck!

For the mattress, try one of those 1-2” self inflating sleeping mats with a foam mattress topper. They both should be pretty compact. The foam helps provide a separation between the cold ground and cold air in the sleeping pad. You may also want a simple thin sheet for day time sleeping.

Coleman 2000016960 Self-Inflating Camping Pad with Pillow https://www.amazon.com/dp/B00BF9IYO4/ref=cm_sw_r_cp_api_ozYyBb6625024

Carpenter 1-Inch Slab Memory Foam Mattress Topper, TwinXL https://www.amazon.com/dp/B003LVY4H0/ref=cm_sw_r_cp_api_oAYyBb38BD114