Will they accept partial pay and extend if I have a court date to pay a $700 fine and surcharge and I only have $450?

Probably. You will have to get the judge to extend your time to pay.

The terms by which a court will accept payment vary from court to court. However, in my experience if you can demonstrate to the court that you are making an effort and will have the full amount within a short time they will give you additional time to gather the necessary funds. Please keep in mind thought that each court is different and your lawyer should be able to tell you what the practice and customs are of the court your case is pending in.