Yes, you can get direct admission to Pune University BCA, after your diploma, provided you meet the eligibility criteria. PU accepts diploma of two years in Pharmacy, and diploma of three years (after 10th board) from the Board of Technical Education authorized by Govt. of Maharashtra or equivalent.
Note that PU doesn’t offer later admission to BCA. You can’t get admission to the second year of BCA, after completion of your diploma.
Yes, you can take direct admission in BCA at Savitribai Phule Pune University. There is no entrance test for BCA. The eligibility criteria required for admission is at least 50% in 10+2. You also should have had Mathematics as a subject in your 12th. Without Maths, you won’t be eligible for the BCA program. If you meet these eligibility criteria, you can get direct admission.