I'll try to answer as much as I can.
It appears you have to shoot a certain ship while it's in formation to trigger the SP "free ship" rally X flag. I've read the postion of the ship or which on you need to shot varies based on your score. If the last two digits of your score read 00 then it's the bottom right second from left ship.
Taken from here:
http://www.cheatbook.de/files/gaplus.htm
There used to be a book called "All about Namco" in
Japan years ago which included the tips, maps, and
everything of all Namco games. It had a few pages about
Gaplus and there was a table showing which bug you need to
kill to get the special flag. I don't remember exactly how
it goes, but it was kinda like this. If your score's 1000
and 100's digits are 00 when the new parsec begins (for
example, when your score is 0000, 10000, etc.), you need
to kill the second bug from the left in the bottom row.
If those 2 digits are 01 like 10100 and 20100, kill the
3rd bug from the left in the bottom row, etc. 03 is the
4th bug and so on. I think it goes all the way to the most
right one in the bottom row, then the 1st one to the left
in the second bottom row. When it gets to the most right in
the second bottom row, it comes down to the 1st one to the
left in the bottom row, then you're back at 00 (2nd bug just
like parsec 1).
Extra ships. If you click on the twin galgiexes link you posted then click on the "rules" link your'll see the explanation of this.
Note: The manual for Gaplus/Galaga 3 shows the default setting to give extra lives at 30k, 150k, and every 600k thereafter. This setting does not exist and the game cannot be set to such settings.
When the dip switches are put to the default positions, they give extra ships at the shown settings above (every 150k) which also matches settings for home console versions of Gaplus for the PlayStation and Nintendo Wii as well as the test screen example shown in the manual on page 4. It is believed that the manual lists settings for a pre-release version of the game and was not updated upon release.
The "Preliminary" manual is the offical one. They never released an updated one beyond that.
The game shows only 4 extra ships below but I've head you can bank up to 8 max extra ships.
You are correct. If you collect all 3 compents you get an extra ship. The Extra bonus stage adds one componet and the Bye Bye bonus stage deletes one componet. The battle head weapons drop from the boss bug ships as well. I've been told if you reach parsec 31 there is a battle head the will change your ship to this must fast and extra fire Hypership you see in the video.
TAS videos are basically edited to look like a single take, and there's a lot of trial-and-error involved. But things like knowing which alien to shoot to trigger the flag is either a LOT more attempts to figure out, or someone looked at the code to see what triggers each one (which would be much easier and faster), because you'd have to keep replaying every parsec and shooting each alien to find the right one. With most of those, the player is hitting the right one as it flies out to get into formation because it's often one that's in a location that isn't in the bottom row.
The challenge stages are even more impressive to see in that video. Overall, the video shows just how hard the game is the further you get into it, which makes the 2 million-plus high scores on Twin Galaxies seem very improbable:
Join TwinGalaxies.com, the go-to place for over 40 years to celebrate video game achievements. Dive into competition, share your wins, and connect with friends in an official gaming community!
www.twingalaxies.com
There's still some parts of the game I don't know. The game says you get a free ship at 30k and 70k and ??? after that, but the manual shows different values depending on the dip switches, and there's no "30k and 70k" combination. The TAS gameplay shows free ships at 30k and 70k. Both manuals on KLOV are marked 'preliminary' (as is the one on crazykong.com) so maybe they're both wrong and the released version has the correct info? The game only shows up to 4 ships in reserve onscreen; does it keep track of more than that, or is 4 the max?
The 'components' you get during the game are the 3 components that comprise your original ship (which you see get 'assembled' at the start of the game). I'm guessing if you get all 3, you get a free ship. During that TAS video, in parsec 19, an alien appears with a component above it, and when it's shot, it falls down into your inventory. The player got another component during the 'lucky' bonus stage (right before parsec 29). During the 'bye bye' bonus stage (right before parsec 34), a component was removed! The player gets another component during parsec 36. At the end of parsec 37, another alien had the 3rd component, which, when it falls down into the inventory, all 3 parts disappeared.