Is it true that there is no custodian fees will be charged for shares bought from the HongKong/USA market?

Not true for all platforms - For example, DBS charges clients 0.20% or a min. of S$100 per half-year for each foreign shareholding/market. So, if you have stocks in US and HK at any time during the half-year, you will be charged a min. of S$200 per half-yearly. Quite excessive - so, be careful. Better to trade elsewhere if you want to trade foreign stocks.

Yes but there are dividend handling fees for US market which can eat up alot of ur returns if you are starting small and focus on dividends.