As you fly on normal everyday line operations generally the legs YOU fly you log as p1/s or PICUS. BEFORE you log these legs as PICUS you should check both your OPS manual and with the captain to ensure that this is acceptable. Then at the end of the days flying you should ask the captain to initial your logbook. Failing this some authorities will accept a written letter from your companys chief pilot stating that they have reviewed your hours and that they are correct.
Sim time does not count towards your flying hours. You can keep a note in a memo column of these if you so wish but the only thing they count for is licence issue.