I have the following clarification.

1. After getting admission and if one gets married can one go to US and study in H4 visa.

2. Is there any waiting period for persons in H4 visa to study - only after one year of stamping one can join a university for full time study.

3. I understand that persons with H4 visa can pay reduced fees as applicable to residents. Is it true. If so can one get the benefit immediately or has to wait for one year.

1. After getting admission and if one gets married can one go to US and study in H4 visa.
If you don't have any visa by the time you submit the application, you must go for F-1. If you already got H-4 visa, you can choose if you want to go for F-1 or H-4.

2. Is there any waiting period for persons in H4 visa to study - only after one year of stamping one can join a university for full time study.
No waiting period, you can go to school as soon as you get your visa.

3. I understand that persons with H4 visa can pay reduced fees as applicable to residents. Is it true. If so can one get the benefit immediately or has to wait for one year.
No... both F-1 and H-4 are non-immigrant visas, so you are categorized as aliens, no reduction in tuition fees. Those who get tuition fees at residents rate are greencard holders.