Can sinus infect (confirmed xr) cause slightly enlarged bilat posterior cervical lymph in children? all smaller than 1cm, how long till they shrink back

Definitely: Some glands will resolve when infection clears up.Others stay longer for months and years. Remember, children get colds several times a year and on top of it get ear infection, throat infection etc , thus lymph nodes stay swollen/enlarged much longer.

Yes, almost always!: This is almost the rule, not the exception. Assuming the sinus infection clears, enkarged nodes may last for 4 weeks or more, because of the infectious debritus still in the system.

Sometime occurs : These nodes can be slightly enlarged off & on throughout childhood from things a diverse as a bug bite or drainage in the throat. They have little significance.