REPLY FROM UNCLE AGONY
Unless the contents of the books you are importing contain pornographic materials, contain obscene materials and/or contain seditious materials you may import them freely. However you would need to pay import duties and you may wish to check the specifics with IRAS before you embark on your enterprise.
As for publicizing your own book, you will need a permit to publish it if you are in Singapore and you can check with the Ministry of Culture.
However as you mentioned you would still need a distributor. Normally the local publisher would take care of that for you. If you do not have one, you may have to go through book sellers one by one. That is if you intend to sell your book the traditional way. The question of distributor does not arise if you are selling through the internet.