Q: What programming languages are available?
A: Anything that'll run on a PC-XT, including various flavors of C,
C++, Pascal, Basic, etc.  QBASIC.EXE is not included, but will run if
it's copied from a MS-DOS 5.0 machine.

There are several ways to write "programs" with software in the
100/200LX ROM, depending on your definition of a program.  You have
the keyboard macro application, Lotus 1-2-3, the calculator's solver
application (finds roots of equations, among other things), DEBUG.EXE
(from DOS), and the DOS batch file interpreter.  The calculator's
solver application can be used with Lotus to "backsolve", that is,
adjust the value of one independent cell of a spreadsheet to produce
a desired result in another, calculated, cell.

Q: How can I get information on programming the internals of the HP?
A: The palmtop Developer's Guide is being distributed by Thaddeus
Computing (publishers of the Palmtop Paper).  Price is $79.00 US,
plus $5.00 shipping inside US, $12.00 shipping outside US.  It
contains full documentation on the internals of the HP Palmtops,
plus software for developing system-manager compliant applications.
You'll need to supply your own compiler and/or assembler (MSC 6.00AX
and/or MASM 5.1 are recommended).  Order from Thaddeus Computing, 
57 E. Broadway, Fairfield, IA 52556 (800) 809-5603, (515) 472-1875,
75300.2443@compuserve.com

For those who don't want to purchase the full developer's kit, there
is a library called PAL (Palmtop Application Library) which is a
collection of C language functions that provide DOS programs with the
look & feel of HP100/200LX built-in applications.  It provides
graphics functions, support for windows, menus, dialog boxes, etc.
It is free, and available on the HPHAND forum on CompuServe, as well
as ftp.monash.edu.au, eddie.mit.edu, and butler.sidewinder.com.

Many of the HP's interrupts are documented in the interrupt list,
maintained by Ralf Brown, available at
<ftp://oak.oakland.edu/pub/msdos/info/interNNx.zip> and elsewhere.

Of course, if you only want to program the HP as a DOS machine,
without accessing any of the palmtop's unique features, there are
plenty of widely available books giving details on DOS programming.

If you need the file formats for the built-in applications, gdbio (on
eddie) has C source code which should provide a good starting point.