Sounds like you are planning a very intersting trip.
Couple of things to consider.
1. Indonesia is incredibly safe. The people are generally very poor but an integral part of Indonesian culture is the care of travelers. No matter where you are in Indonesia if you need a drink, a meal or somewhere to sleep you can find it. Nobody expects anything in return and you will find that the local taxi driver will help you find the right place, you may even be invited to his home for the night. If you get that chance, take it. You will never find warmth and hospitality the same anywhere in the world like it. If you want to give something in return, teach their kids some english, buy some chocolate, take some photos of them and get them developed at a local Fuji Film processing.
2. Accommodation is usually basic once you get below the 4 star hotels. Even 3 stars hotels in Indonesia are very very basic. You will see many other backpackers and Caucasians everywhere in Indonesia, so if you need advice just ask, all of us who spend a lot of time there will help you no matter how busy we are. Indonesia is that sort of place.
3. Help. The police generally are not helpful. If you are lost of just need to know something, look for a mosque. There is always someone at the mosque and they will let you rest, give you a drink or food and find someone who speaks English to help you. Again, the police are NOT helpful.
4. Language. You will be amazed at how many people, especially the younger ones, speak English in INdonesia. But language is not an issue to communicate with Indonesians, life is made up of very simple elements. And there is always someone close by who can speak enough English to help you.
5. Transport. The train is ok, but its unreliable, incredibly slow. It will certainly be an experience. but dont book too cheapop or you may end up having to stand up for 12 to 15 hours. You can usually hire a Kijang (like a MPV but rougher) for a reasonable fee. Whereever you are staying someone will know someone who is traveling somewhere and you can usually hitch a ride for a few dollars and a promise to buy dinner for everyone, it will cost you about $2 each person.
6. Places to visit. Surabya has nothing offer apart from ease of transport. You want to go to Jogjakrta and Borobudur if yuo are in that part of Java, avoid Surabaya. Jakarta is worth going to just for the experience, its huge. Not a lot to see but a couple of days is enough. Plenty of tourist information and a great nightlife. East Java is very beautiful too, but not a lot of time is needed there. If you get a chance to visit Sumatra you will be very pleased to see how different it is, Padang, Palembang and then up to Danau Toba, you will love it. And if you are feeling adventurous try Aceh, dont believe the crap on the government websites., Aceh is one of the safest and most friendly places in the whole world. They actually speak better English there than the rest of Indonesia and its really really beautiful with Orangatans, monkeys, all sorts of wildlife and maybe even a Sumtran tiger (there is about 300 left in the wild).
Boat from Batam to Signapore, yes its possible but you have to fly to Batam first, probably cheper to just fly from wherever you are to Singapore, Batam is not going to be of interest to you after seeing everything else.
Good luck, go with an open mind and a big smile on your face. You will never regret it or expereince anything like it again