B.A Entrance Exam

No, it has a merit based criteria of admission.

You first have to clear their entrance exam. You can study NCERT books, it is quite helpful.

Yes, with this rank you can get admissions there, and if you have any queries do let me know write down the comments below. All the best for your admission.

Before preparing for any exam first you have to understand the test format after that you can check the study material. Mock test is very important because it shows were you stand, in mock test you can understand your weakness and strong points and also it's helpful for time management.

Here is the syllabus:
Ancient History
Classic Antiquity
Middle to Late Bronze Age
Before Christ
Greek and Roman Civilizations
Early ancient History
Timeline of Ancient History
Late Ancient History and Post-classical History
Early Iron Age
Prehistory
Chemical Preservation of Monuments and Antiquities
Museology
Epigraphy and Numismatics
Application of Science in Archaeology
Principles and Methods of Archaeology
Structural Conservation of Ancient Monuments.

B.A. Entrance exam syllabus is varies from college to college, however the following books and methods can be helpful in entrance preparation:
1. For general studies, you should study Lucents General Knowledge.
2. For mental ability, you can choose Arihants Reasoning Book.
3. You should read newspapers for Current Affairs.
4. You should have knowledge about all the books, e. g. , Science, history, geography, economics, civics, from 6th to 10th.
5. You should have sufficient knowledge of English Literature and English Grammar or Hindi Literature and Hindi Grammar of Intermediate level (11th & 12th).

You can take coaching, or you can purchase a book and read thoroughly.

BA exam is on 11 & 12th April. & BSC is on 7th April.
BA:-
The exam will be held across 22 cities of the country. Admit Card for the test will be available from April 11 and 12, 2019 on official website of exam.
BSC:-
AMU B.Sc Hons Entrance Exam 2019 date announced; Exam on 7 Apr 2019. Aligarh Muslim University(AMU) has now released the examination date for the AMU BSc Hons entrance examination. The entrance examination for candidates taking up B.Sc Hons from AMU will be held on April 07, 2019.

No, students who attend TISSNET have to clear then overall cutoff of that particular course.