I received a letter from child support office asking if I would like to have a child support review.
You did not "receive a letter from child support." I assume the letter came from the local child support enforcement authority ("CSEA") because you, at some point, requested that the CSEA handle the collection of support, instead of having your ex-husband pay you directly by writing checks.
if I want to puruse the increase, what do I do?
Talk with someone at the CSEA to see if the CSEA will pursue the increase on your behalf. Otherwise, you'll have to file the appropriate paperwork with the court.
if it turned out that he should pay less, and I dont agree, and he wants to take take me to court, what do I do?
What do you do about him wanting to take you to court? I wouldn't concern myself with what he might want to do. If he files papers for a reduction, then you'll have an opportunity to oppose his request.
Do I need a lawyer for this negotiation process?
What if it turned out I make more than him (just himself not his household), will this impact the consideration?
I'm not in your state, but I assume your relative incomes are part of the calculation.
If he takes me to court, do I have to go? What is the consequence if I dont go. Can I just not show at the conference if I really want to avoid all this, or it will be a bad record for the future?
What does "takes me to court" mean? If he files papers to reduce the support payments, you'll have an opportunity to file papers opposing his request. Presumably, the court will hold a hearing (but maybe not). If it does and you don't show up, the court will issue a ruling based on the written submissions and any oral argument that your ex or his attorney makes.
As for the "conference," if you requested it, it would be rude simply not to show up and, if you do so without telling someone ahead of time, you could be sanctioned.