Sorry to hear about the recent setback but don't despair! To qualify as a psychologist is a long and arduous process, with multiple hurdles but if this is your dream or passion then the perseverance is worthwhile.
You did not state at which point in the process you currently are, although you did refer to "beginners". There are two methods of qualification (1) the B.A./BSc. degree, Honours degree, M.A./MSc. degree route which corresponds to a minimum of 3, 1 and 2 years respectively or (2) the DPsych. route which is basically a pre-graduate degree followed by a second degree which culminates in a doctorate. Route (1) has a PhD as a optional addition following registration. I am speaking under correction but I believe the DPsych route takes a minimum of 7 years. The last year of formal training for both options incorporates a 12 month internship and following both of these routes you will be required to complete a 1 year community service year, submit a research dissertation/thesis and pass a National Board Examination. Upon completion of all of these requirements you can register as a psychologist within your registration category at the HPCSA.
I am not very familiar with the DPsych option so will limit my points to Option (1). At pregrad level acceptance is based on your matriculation marks. To my knowledge no specific subjects are required but obviously Science and Mathematics will be beneficial if you opt for the BSc. instead of the B.A. Linguistic abilities and an aptitude for abstract thought will be helpful. Strictly speaking, this portion of the process should not be too difficult provided that your matriculation certificate allows for university exemption and adequate marks.
Once this first degree is completed, you can apply for entrance into the Honours course. Historically, acceptance here is limited to the top students as defined by the number of places available. If the university has 200 places they will take the 200 students with the best 3rd year Psychology marks from the B.A./BSc. group. It is therefore important to ensure that your final year pregrad marks are as high as possible.
Upon completion of the Honours degree, you will apply for Selection (M.A./MSc.) at various universities. Again, with recent changes I may be a bit out of date but previously applicants were required to send each university they were considering an application that included your Honours marks, a personal and "professional" CV and two or three references. Based on this, the university would invite an applicant to the Selection process. Although academic marks are not as important here as in Honours selection, the better the marks the more likely you are to stand out and be remembered. This Selection varies from university to university but typically lasts between 3 and 5 days. It involves a process of elimination whereby personal interviews, group work, role play, panel interviews can all be included and the list is posted at the end of each day reflecting those who have "made it" to the next round. On the last day a final list is posted which shows those who have been selected for the next years M1 group. Kind of like Survivor, just not as laid back! Typically a university will receive approximately 150+ applications per year, of which they may invite say 30-50 people, of which 8 to 10 will ultimately be selected. Again, every university differs slightly in their process. It is important to apply at various universities as you may not get invited to one, fall out in Round 2 at another but get selected at a third.
Rule of thumb "back in the day", if you were invited to selection and/or you progressed to Round 2 then it was felt that you should keep trying as there are a number of variables involved including group dynamics so maybe this just wasn't your year. My favourite urban legend is regarding the tenacious guy who attended 11 selection processes (that is, over 11 years)... he was accepted in the 11th year. Many people get accepted in their second or third attempt but it is a personal choice regarding how many times you want to go through it.
Regarding your second question; at pre grad and Honours level, ensure that you achieve the best marks that you can. With regards to the last "hurdle", you can show your dedication between annual selection processes by building up your CV. Attend courses independently, volunteer at LifeLine after completing their training course, offer psychometric services, get involved in counseling services at your church (even if it is not as a counselor per se), approach the SA Depression and Anxiety Group offering your services, go and see Children's Homes to enquire whether they could use some extra assistance, contact local psychologists and ask about testing, volunteer at a hospice, find work that involves interviews, placement, training, presentations all of which will strengthen your position at the next Selection. Life experience is as important as work experience. You can ask the university for a list of recommended reading or you can visit your local university bookstore. They stock all of the prescribed books for the next year and you can start reading those which will definately give you a head start. Online there are many psychology forums which you could follow to get a feel for the type of problems that clients/patients will be dealing with and/or the type of approaches that therapists/psychologists will be using to assist them.
Best of luck with your journey, wishing you every success with your next application.