To visit these countries you need a visa. Depending on the country of which you are a citizen, a different package of documents is provided. If there is a short-term visit to Singapore, you can get by without a visa, because visa-free transit is possible within 96 hours with an air ticket to a third country.

In Taipei (the capital of Taiwan province) there is a diplomatic mission of Singapore, visa issues for visiting this country.

Consulate of the PRC in Taiwan is not, with the practice of issuing visas on the Chinese border for citizens traveling from Taiwan. But getting permission to enter the country is problematic and not guaranteed. It is better to apply for visas to China and Singapore in advance and in Russia.