please rec some shoujo manga where the fl has a lot of faults but the ml loves her regardl...

not sure if this will hit the mark in the way u mean but
https://www.mangago.zone/read-manga/jishou_akuyaku_reijou_na_konyakusha_no_kansatsu_kiroku/

Enjoy
https://www.mangago.zone/read-manga/sukinako_ga_megane_wo_wasureta/
https://www.mangago.zone/read-manga/i_stole_the_male_lead_s_first_night/
https://www.mangago.zone/read-manga/always_a_catch/

https://www.mangago.zone/read-manga/yamase_wa_doko_e_itta/