Actually that's the best option when you are planning for a solo trip. You can personally check out the options available and select your budget hotel.
Malaysia you can do..But for Thailand and Singapore visa you need to show them your hotel bookings.So you need to prebook your stay.You can do that in booking.com without paying later which you can cancel free of cost.
Yes, you can if you have the time and money. Thailand has visa on arrival, while for Malaysia and SG you need to take one in advance (Malaysia has VoA, but very expensive and not worth it). Infact all three countries are very diverse and different and you will not feel bored at all. Thai has a unique culture and is very famous for it’s night life, pubs and thai and ‘you know what I’m talking about’ massages. If you have never experiences the in your face sex and night life, Bangkok, Pattaya is a place to visit. If thats not what you are after, then there is enough cultural places and great shopping too! Malaysia like their tourist moto is truly asia. Beautiful culture, amazing cave formations, pristine forests, beaches and dive spots. Amazing food too. Singapore is truly the east meets west country/ city. Absolutely clean, modern and yet holding on to the Asian charm. It’s a city for great shopping and the best foody destination in south east asia, if not all of Asia. I suggest you do Thai, Malaysia and SG in that order to appreciate the difference in culture. You will also start from the most welcoming country and sign off from the best airport in the world!
For Singapore Thailand and Malaysia you can book hotels via booking.com pay later and free cancellation option . my suggestion is you make a confirm booking to Singapore and Malaysia before hand so that visa process gets easier.
For Singapore and Malaysia , you need to show your hotel booking before applying the visa or any friend or relative address proof , in the case of Thailand you can skip the booking of hotel in advance.