I'm so sorry your doctors are communicating more to you.  I found at the beginning it seemed like they didn't want to tell you too much to overwhelm you but it seemed I sometimes felt I needed to know more.   Here is my best explanation of the stages.

Induction - lasts 28 days - during this stage the point is to get your child into remission.  You can't move forward till remission

Consolidation - lasts 28 days - this stage is targeted at killing off any cells that hid in the spinal fluid.   There are weekly spinal taps.   you must have an ANC of 750 and platelets over 75 to move past this stage

Interim Maintenance (IM) - lasts 8 weeks - this stage is a bit of a recovery stage before Delayed Intensification.   However the protocal was changed where you get IV Methotrexate in escalating doses sometime around a year ago.   You must have platelets over 75 and ANC over 750 to continue past this stage

Delayed Intensification (DI) - lasts 8 weeks - however divided into 2 - 4 week periods.   This stage is suppose to deliver the final BIG blow to the leukemia cells in the body.   Each stage has a different "cocktail" of chemos.   This along with induction were the two toughest stages for my daughter.  You must make "counts" - ANC of 750 and platelets 75 to move on to each separate period.   Delays are VERY common here.

Long Term Maintenance (LTM) - Lasts the remaining time.   Your end date is calculated at 2 years after you started IM if you are a girl and 3 years after you start IM if you are a boy.    This is a 12 week cycle that repeats over and over.   Within that 12 week cycle there is a 4 week cycle that repeats 3 times.   Basically every 12 weeks there is a spinal then every 4 weeks there is a 5 day pulse of steroids, weekly dose of methotrexate, and daily 6 MP.   They try and keep ANC between 1000-1500 ideally.   There is a little bit of an adjustment period to find the right dose.

You mentioned counts.  My daughter has had a bad time with counts as it sounds like your child is having.   Most people are delayed some in DI.  However we have experienced delays during every stage.   I think we were delayed 3 1/2 weeks after consolidation, 4 weeks after IM, 6 weeks after the first half of DI, and 4 weeks after the second half of DI.   In LTM we have had a 4 week delay and a 2 week delay so far (we only started in Aug).   So, it just depends on the child.   Typically they don't worry too much if you are always delayed.   Our first delay was very hard and stressful however now we just expect them.  I'm actually shocked if she has good counts.  We have had one Bone Marrow biopsy to make sure our delays were just due to sensitivity to chemo.   They consider these after 3 weeks of delay.

You also mentioned neutropenic precautions.   You will find on here that the recommendations for these precautions varies greatly.   Our daughter has been neutropenic for MONTHS!!!!  So we take a middle of the road mentality.    An ANC of below 500 is severely neutrapenic.   At this level we don't let her eat fresh fruits and veggies (unless I can peel it), no leftovers, all the other restrictions they throw out there, and we don't take her out really anywhere.  Above 500 we let her eat whatever but we do waah everything.   From 500-750 we go out and about but try to avoid crowds.   Above 750 we don't have really any restrictions except good handwashing and staying away from sick people.  

Our clinic distinguishes some at below 250.  This is the level that I don't let anyone come over but just family and friends I know aren't sick and I only let a few come over at a time.   I'm also SUPER strict on the foods.   Our doctors have said below 250 is the extremely critical level.   However really below 500 is very low and you have to be careful.

Good luck to you.   This is probably more than you ever wanted to know.   Also my daughter is on study so your protocol could be a little different.

Larisa