I. Japan is investing in strengthening bonds with ASEAN countries and Japanese countries recently won a $ 370 million contract to start .......... a new underground railway system in Jakarta.
II. The cost of ......... space vehicles is high no doubt, but the costs of complying with legal and regulatory paperwork and rules is huge too.

Here construction, manufacture and building have same context.
But only 'building' can be used as it gives the sentences gramatical coherency.
THe statementb would read  as:
I. Japan is investing in strengthening bonds with ASEAN countries and Japanese countries recently won a $ 370 million contract to start building a new underground railway system in Jakarta.
II. The cost of building space vehicles is high no doubt, but the costs of complying with legal and regulatory paperwork and rules is huge too.

Option E is correct option.