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Visa: It depends on how long you are staying in each country in your case. On this website you can look if you need a visa or not: http://www.doyouneedvisa.com/
About the return ticket: If you have a flight ticket out of the country you'll be safe eventhough it's to another country where you came from. If you don't have booked the tickets yet when entering the country, I'm not entirely sure.
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You need a confirmed departure from whichever country you will first enter, be it Thailand, Malaysia or Singapore. All three countries allow visa free entry, but for a limited time period and if you can not show that you are leaving the country before that time expires, the airline flying you there may not let you board.
Please know that this "proof" is pretty much limited to a confirmed air travel booking. A bus ticket to the border will not suffice. A train ticket across the border (Thailand-Malaysia) might work but not always.
Similar rules exists within SE Asia when going to your next country, though these tend to be not as heavily enforced, BUT still are on the books and you could be subjected to the text of the law.