I was in the care of a CNM and her staff my whole pregnancy.
The first and second trimester the nurses would check my urine, weight, bp, heart rate, temp and then the midwife would come in and check the baby's heart rate and answer any questions of mine. I'd get the blood panels once every 3 or so months to see how my levels were.
Around the start of my 3rd trimester it would be the same procedure with the nurse, then the midwife checks baby's heart rate, but then she checked my fundus height and measured. The only time she did a cervical check was when I was 1 week overdue and she was sweeping my membranes to get labor started.
I figure that midwives are very hands off and noninvasive. They know that there is no need to check your effacement or dilation unless you're in labor since it could possibly kick start labor and they want things to take a natural course.
I worried about this as well since I thought they were supposed to check, but I'm glad she didn't until she felt the need.
I guess it all depends on you. I didn't really want to be checked (although in the back of my mind I did since I was curious), but I prefer noninvasive.
My midwife checks urine, bp, baby's heart rate and starting at 29w they measured fundal height. There is no reason for a cervical exam until you're going into labour.
Flu symptoms should definitely be checked by a doctor, not a midwife, that's not what they're trained for.
There's no reason for them to do cervical exams til you're around 36 weeks...