Which route should I go through Asia?

1. Do you normally climb mountains when at home? Do you normally do at least moderate amounts of exercise? How will you keep your fitness up between July and September when you plan to do your first real mountain climb?

Unless there's some other difficult way to do it, climbing Gunung Bromo is dead easy - my 75yo Mum climbed those stairs in about 20 minutes (of course coming down was harder because you feel like you're going head-first).

Personally, I don't see the point in climbing a mountain. To me THEY are the view from the ground. Also, in Bandung the closer Volcanu (Prahu?) you can actually DRIVE up to the top of. It's wonderful to see, because you are looking into an active volcano, but there's a carpark at the top and stalls around the sides. Not sure about the volcano in the opposite direction as that is a separate daytrip.

1. I reckon you're trying to do too much in Malaysian Borneo if you want to trek in Mulu NP. Also you will either need to fly or find out if you can get a visa at the land border (when I was there, Australians couldn't) when going between the two Malaysian states, because Brunei is in between them. Personally, I'd stick to just Sarawak in Borneo as there's lots and lots to do there. If you are up near Mulu NP you could try to get to Bario which is a pure slice of heaven (and little visited) - it is a plane ride but it's easy to book the day before and used to cost about $30 o/w. BTW once in Bario you can do some amazing trekking, too, if that is your interest.

The more you move from one destination to another the higher the cost. If you are allready above budget then I would suggest you cut some destinations. You need to be below budget before you start and it would be a great idea to carry a buffer as well. Travelling is great, but not much fun if you are penny pinching all the time. I reckon you want to stay in pretty basic accomodation to save money, but then it´s great to treat yourself to a more upmarket place once in awhile as well to make it bearable in the long run.
Travelling can also be very tiring and it´s a good idea to build in little breaks once in a while where you stay put for maybe a week and let yourself relax completely and maybe even become a little bit bored. That break can be anywhere like on an island where you don´t do anything else than eat, snorkel and read in a hammock or in lovely Luang Prabang.
Your one month to cover Bali (which is pretty expensive compared to rest of Indonesia), Lombok, Flores and the Komodo Island is very very rushed. I would either cut out some stops or extend your time there.
Singapore is really expensive and july is not the best time of year to be there, I would cut Singapore down to just a few days.
These countries won´t disappear, so travel a bit slower and then come back another time to travel Vietnam or the Philiphines might save your budget.
How much do you need and how much have you allocated per day?
Don´t forget to add insurance and vaccination cost to your budget.

I like pia2am's comments about building in little breaks. I reckon you need to take at least a few days away from constant moving at least once a month. Think about it - at home you would have two days once a week to recharge. Long journeys, constantly getting used to new surroundings, and packing lots into your day are all very tiring.

I didn't notice the week that you have allocated for Singapore. I know that it's your first destination, but it's quite similar to, but not as interesting as, Malaysia, and a whole lot more expensive to boot. I've spent 6 months travelling around Malaysia, but have only spent a couple of days in Singapore because of this. It's just not worth spending a week in Singapore (unless you know someone there that you are visiting).