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With scores of 82 in Maths, 87 in Physics, and 45 in Chemistry, you might still be able to get admission to a good engineering college, but your chances for top-tier institutions might be limited due to the relatively low Chemistry score; you should consider applying to colleges with a more lenient admission criteria and focus on performing well in entrance exams like JEE Main to compensate for the lower Chemistry marks.

Your high scores in Maths and Physics demonstrate a strong foundation in key engineering subjects, which can be a positive factor for admission.
A significantly lower Chemistry score might limit your options for top-ranked engineering colleges, as most programs require a balanced performance across all Science subjects. 

Focus on entrance exams:
To improve your chances, prepare well for entrance exams like JEE Main and state-level engineering exams, where your overall performance across all subjects will be considered. 
Explore colleges with lower cut-offs:
Research colleges with slightly lower admission criteria, which might prioritize your strong performance in Maths and Physics.
Depending on the engineering specialisation you choose, the importance of Chemistry might vary. Look for fields where Maths and Physics are more heavily emphasized.

Several Indian colleges and universities offer integrated M.Sc. programs, and many are now accepting CUET (Common University Entrance Test) scores for admission. Some of the prominent institutions include the University of Hyderabad, Banaras Hindu University, Jawaharlal Nehru University, and various central universities like the Central University of Punjab, Central University of Jharkhand, and Central University of Tamil Nadu. Additionally, some state universities like Guru Gobind Singh Indraprastha University and private universities like Amity University and Shoolini University also accept CUET scores for their integrated M.Sc. programs. 

Like any other language certification, they are useful if your career or academic life requests it. Usually the HSK is mandatory if you have aspirations of studying in China, and some jobs might see having an HSK a somewhat proof of your proficiency (but then again, its not that common, usually they validate it in other ways). So, if you plan to study in China, check the university requirements for enrollment and take the HSK basing on that. If you plan to take on jobs that require mandarin as a language, take the HSK as a initial proof of knowing (but then again, not super useful, its more of a starter).

No, it's not bad knowing only simplified.

Thapar Institute of Engineering & Technology (TIET) provides a three-year BBA degree course under Thapar School of Liberal Arts and Sciences. It is provided by means of an online aptitude test and a personal interview. Aptitude, logical reasoning, general awareness, and analytical ability are tested through the aptitude test. The candidates with a minimum SAT of 1,260 and above are exempted from the aptitude test and can sit for the personal interview. The course is specialized in fields like marketing, finance, operations, human resource management, etc. 
The total fee for the BBA course is around INR 14 lakh.
For current information related to deadlines and application information, it is advised to check with the official website of Thapar University or speak with the admissions department.