Fly to Kota Kinabulu and then to Tawau.  Lots of flights to KK.

Sorry, I don't know but I doubt it would be expensive.  It only cost me $200
Cdn to fly to KK from Singapore.

Why do you want to go to Jakarta?  That place is a pit, AFAIC.

How long do you plan to stay S'pore, if you go?  It can be done reasonably
inexpensively, just not quite as inexpensive as some other locals.

Also, consider asking your question at rec.travel.asia.  The posters there
are a font of info.

Came back just 5 days ago... they will not see me again

Nonsense. If you are in Tawau, there is no point in going south to
Balikpapan (BTW, forget about getting there overland) and then move
back northbound towards Sangalaki. Take a (cheap) ferry to Tarakan,
then a (cheap) flight to Berau. Sangalaki dive lodge will pick you up
at Berau airport (sort of... a couple of groups from Singapore were
left hours at the pier, the boat then got lost on its way to
Sangalaki, had to spend a night at Derawan, but this is another
story... our transfers were ok).

Singapore - Balikpapan - Berau is the standard air route to get to
Sangalaki. Singapore is not necessarily expensive and - depending on
your flight - you might even get an immediate connection to Balikpapan
(check www.silkair.com for their timetable, they have daily flights
and are part of Singapore Airlines). 3 days a week Silkair flies to
Balikpapan early in the morning, just on time for catching the flight
to Berau.

Sangalaki Dive Lodge (SDL) offered us Balikpapan-Berau-Balikpapan
flights, car transfers in Berau, boat transfer to the island, hotel in
Berau on the way back, @ USD 250pp. Found out that flights were much
cheaper than that, yet almost impossible to book outside Indonesia.

Check for price at SDL!!!! I wrote to their email address and got an
offer at USD 190pp, all included; booked through my agent at USD 170;
found out that most of guests were paying USD 150, even for shorter
stays than mine, all the same package.

Diving: mantas, mantas and mantas. And plenty of stingrays, litlle
critters, shrimps, turtles (not as many as in Sipadan) although my
favourite one was a big cuttlefish. Sandy bottoms with healthy coral,
easy dives, max. depth 60ft, low visibility. They will also take you
to the nearby islands of Samama (for the pigmean seahorse, and not
much more) and Kakaban - walls with strong currents, even downwards,
where dives can be challenging; known for schools of barracudas and
big pelagic, although we were not lucky with visibility and saw only
barracudas.

All in one, not to be missed for manta (or stingray) maniacs. Others
might head to Sipadan, Kapalai, Mabul or Layang Layang (don't know
about Lankayan). Sangalaki island itself could be heaven: at night you
can actually fall asleep at the sound of sea-turtles laying eggs near
your cottage.

As much as I loved the island and its diving, the Lodge was a major
disappointment: at first it looked like abandoned, a company which is
about to go bankrupted. Cottages need a major renovation, food very
low on quality and quantity (they even ran out of it one day and did a
great job in recycling leftovers), no fresh water for rinsing your
equipment (let alone showers), no management at all... they
progressively ran out of beer, cokes, tissues. One day the owner
finally arrived from Kota Kinabalu, where he lives, and things
improved a little bit... at least you had no longer to ask for more
food out of the kitchen. He explained that he was to renovate the
cottages, probably in November, and I have personally spoken to an
architect from Singapore who was in charge of the new design.

Someone from the staff was complaining for not being paid for a long
time, don't know whether it is true or not, yet it would explain a lot
of their attitude (no relation with guests, an empty can left for days
where an idiot had tossed it, right in front of the clubhouse, never
got the bedsheets changed in 10 days, no real cleaning). Let's just
say it is very basic, which would be fine for me if the price was too.

Let me know if you need more info, and bring some food of your own,
particularly if you don't love chicken, white rice and prawns since
they are pretty much all I had, every day.