Is it possible to gain global and asset diversification exposure in my portfolio just by buying ETFs only?

Yes, you can. However, returns from ETFs will be limited as compared to directly purchasing the equity directly. As you have stated, management fees will accumuate more so when your entire portfolio is ETFs.

You should look at the tracking error of both SPDR STI and Nikko AM and management fee first. If SPDR STI is lower for both, you can consider switching. Iit takes some time to switch as ETFs relies on DCA and you should not lump sum transfer your ETF.

Yes you can buy other local SG ETFs from DBS Vickers. Do note that there's also charges for storing your units.

You should go for SPDR when possible its slightly better than Nikko. Number 1 you can go for IWDA or VWRD etf for global exposure on stocks. Number 2 im not too sure. There are not much good ETFs in Singapore, even the STI ETF is not that good because they only have 30 companies and they have very high weightage on the banking industries like DBS, OCBC and UOB. Its not really diversified. You need a broker to buy stocks or ETFs. US have more varieties in term of ETFs so dont limit youself to local etfs only because they are not good. You can use Interactive broker or Standard chartered to buy overseas ETFs. I would recommend buying from london stock exchange the ireland-domiciled etf. Because if you were to buy US etfs, it will have 30% withholding tax on your dividends. But if you buy the ireland-domiciled ones, it will be reduced to 15%.