I believe H4 students pay less than those on F1 status. The exact amount depends on the university. However you will not be able to do any on-campus (or off-campus) jobs on H4.
GRE, TOEFL may be required for admission to the university. It is not necessary for applying to F1, given you can get admitted into the university without them. The admission process is almost the same as if you were back home. You need to send in at least the application, fee, transcripts, recommendation letters and statement of purpose, as far as I can remember.
All the best!