If you make a succa like a tepee or bent it towards a wall, R’ Eliezer says it is posul as there is no roof. The chachamim say it is kosher.

A large reed mat, if made to sleep on is considered a utensil which can become tamai and therefore can not be used for sichach . If you made it specifically for sichach, it cannot accept tumah as it is not a utensil and is therefore kosher for sichach.

R’ Eliezer says there is no difference between big mats or small mats.

Succa 2:1

If somebody sleeps under a bed in a succah, he has not done the mitzva. Reb Yehuda says the custom before the times of the sages was to sleep underneath the bed and they did not tell us anything. Reb Shimon says there was a story with Tuvi, the servant of Reb Gamlieil, who slept under a bed in the succah. Reb Gamliel said, ‘Did you see my servant, who is a wise man, who knows that servants are not obligated in the mitzva of succah and therefore slept under the bed.’