At LKYSPP, with regard to environment and energy, you can find courses such as
Environmental Economics
Natural Disaster and Climate Change
Urban Transport Policy
Sustainable and Livable Cities
Water Policy and Governance
Air and Water Pollution
Besides the above, one can feel free to choose an elective from other schools in NUS and people do go to school of design, environment studies etc. There is Institute for Water Policy, a research think tank at LKYSPP that is very resourceful and does some great work.
As far as career services is concerned, let me be very honest - Not just LKYSPP, but most schools including US and Europe do not offer an in campus placements or assured jobs. The career services does lot of networking events, there are career fairs, industry nights that are organized in every semester at LKYSPP. It also comes down to how a student leverages these opportunities and convert them into a job, there are students from outside SG who found a job immediately in SG and there are people who went back to their home countries and there are people who struggle to find the right job immediately upon graduation. This is very much applicable to all top schools. You have all kind of possibilities happening. The Bottom line - The school has a brand, there is strong alumni network, the opportunities to meet people from the industry and network are many - now its upto the student.
Hope this was helpful and All the Very Best to everyone out there. Cheers