advice and tips to look for a banking job in Singapore? is standard one, either you polish your resume or apply direct to the bank, if want better chance, find an insider.
Does how the market affect you coming down to work in SG? i guess the thing you want to know is does it worth change from malaysia to singapore right? this one is depend on yourself, i got some friend worked in malaysia before and coming down here to work, one very enjoy his work here and another work with alot stress.nobody can give you exact advise unless you tell them specific company and role, then someone worked on that post before can answer you.
if your cousin can help you, that is the fastest way and more reliable compare to apply online yourself. you can settle with that job first, feel the environment then you can roughly get the idea how is the environment on different field.

What position you're looking for? I've a contact of an agent whom has many job opening for banking & financial sector.

Hi there. I am in corporate banking.
It is maybe quite difficult to get a corporate banking RM job for someone fresh from Malaysia as you are deemed not to have contacts (same in my case) so I started in SG as a credit analyst.
2 years later still a credit analyst and still deemed not to have to contacts in the industry although i am more than capable of hunting.
Thinking of going back to malaysia to assume a corproate RM role as its more interesting than pushing credit papers, full time.

Further, in SG the sector is very different.
1) Majority of banks (except local and jap) don't want to take balance sheet risk. So they focus mainly on the NII (treasury, trade (non-funded) FX, structured products etc). Competition for business is very very keen as there are more than 30 banks (wholesale and offshore) trying to get a slice of the NII business while very few of them can provide balance sheet to the customers. So if you want to join a bank make sure you join one that can take balance sheet risk or one that has strong product offerings.
2) The local Singaporean market is dead slow these days (be it MNC or local large corps) arising from slow macro economy and trading. Singapore relies mainly on trade as it is an entreport. Try to join one that has regional coverage. Regional coverage in India and China are good bet as there are many business opportunites.
3) Many banks here are doing restructuring/reorganisation/lay-offs etc. Competition is very keen and if you miss your targets you will be let go. Try to avoid american/uk/small offshore banks as they are known for it.
4) Consumer banking is a whole another ball game alltogether. But once you enter, it is unlikely that you will break into corporate banking. But currently I think consumer banking is doing better than corporate banking as SG generally still have high disposable income and savings.
5) Credit is stringent in most banks. The credit quality here is very good (I came from a local bank in Malaysia). Comparatively the credit quality in Malaysia look like kids work esp with regards to cashflow projection, research reports, etc. There are also more sophisticated products in SG as compared to Malaysia.
6) Pertaining to your question of banking being protected agaisnt foreigners the answer is no but they are rumours that MOM is looking into it. Everytime I go for lunch near a certain bank, I get confused whether I'm in India or Singapore.