The correct statements regarding the Neem tree are 1 and 3, thus the available option "1, 3 and 4 only" cannot be validated as accurate since it references a non-existent fourth statement.

Statement 1 is correct as neem oil, derived from the seeds and leaves, serves as a natural pesticide, effectively controlling various pests due to its active compounds, making it environmentally friendly. Statement 3 is also correct; neem oil has significant applications in the pharmaceutical industry for its anti-inflammatory, antimicrobial, and antifungal properties. However, statement 2 is incorrect as neem seeds are primarily used for producing neem oil and not specifically for biofuels or hospital detergents at a commercial scale. The understanding of these applications reflects the importance of traditional medicinal plants and their roles in sustainable agriculture and health, which are critical themes within UPSC syllabus focusing on environmental conservation and traditional knowledge systems.