In my experience, the Portable needs a good battery present for reliable operation, as you have found. Without the battery, it's a bit "hit and miss". You can get away with a 6v "gell cell" battery and jumper wires in a pinch, although the wires need to be fairly heavy duty. Re-celling the battery is not particularly difficult - it contains three 2.0v "Gates Cells" (now known as "Cyclon" cells, I think). Last time I re-celled my Portable's battery, I didn't have much trouble tracking a set of these down.
Being a lead-acid type battery, I advise taking the battery out of the Portable and storing it separately if you are putting the computer into storage for a while. This stops the computer discharging the battery, so the battery will stay in good health.
The 9v backup battery is only used to keep PRAM and SRAM memory alive while you swap from one main battery to another. It is mechanically switched in by a micro-switch on the battery cover. For this reason, the battery cover should always be left in place - if you leave it off, the 9v battery goes flat very quickly.
When considering the quality of the LCD, you must take comments in context. The quality of displays in the late 1980s was truly awful. You might think the non-backlit Portable LCD is hard to read, but compared to other displays on the market at the time, it was truly stunning. "Portable" was also a relative term. The IBM PC Portable was a massive and very heavy machine - the Mac Portable a lightweight by comparison. (Byte magazine had a picture on the cover of the original PC Portable being carried, with the floor collapsing under the user!). At the time, I had a colleague who walked to / from work every day and carried his Mac Portable. It was at least a 1 mile walk each way... carrying "a suitcase" ! When I later bought a backlit Portable, he maintained that the non-backlit LCD was superior, particularly in that it gave a much better battery life. I preferred the backlight.
[EDIT] Holding the reset and interrupt buttons in at the same time resets the power manager and is usually required when the Portable has just had a battery put in after being powered down completely for a while.
It is possible to make your own adaptor and install a different hard drive. At different stages in its long life, mine has had a standard 3.5" third height drive, a 2.5" 80GB hard drive and now a 128MB compact flash card (silent = yay). I posted a photo of this setup in this thread:
http://68kmla.org/forums/viewtopic.php?f=10&t=4477&p=58031&hilit=+portable#p46818
Beware if connecting lots of external SCSI devices; the Portable doesn't supply termination power and doesn't have a "full" SCSI terminator onboard. One other thing: at the time, the 3.5" / 1/3 height drive was revolutionary - the 3.5" 1/2 height drives were considered small at the time, so the 1/3 height drive seemed tiny and extremely high tech by comparison.