Do I need to interact time varying controls with group participation indicator in triple Did?

[Sara George]

hello I am running a triple DiD with female a s a group partcipation indicator
Here

gen treated =treatmentgroup*post
gen treatedfemale=treated*female
reghdfe  `y'  treated treatedfemale  , absorb( female HHPBASE SURVEY COTOTAL5#female Nchildren#female  district_id#c.SURVEY#female) cluster(IDPSU)

I have two questions

1.Do I need to interact the time-varying covariates COTOTAL5 Nchildren with female?
2. Is it okay to interact the district trend with female?