First time posting, so sorry if this stuff has been answered elsewhere, but I have a few questions. Hope you all can help...
Insect spirits are covered pretty completely in the Street Grimoire, starting on page 93. With that said, I'll answer what I can from the book.
1. Does a Hybrid form retain its spirit powers? What about a Flesh Form? Or do they just get the vessel/host abilities plus a few?
This is covered in Street Grimoire, page 196.
The hybrid form’s physical attributes are enhanced by the spirit’s Force. The spirit retains all of the host’s natural abilities but only some of its memories and none of its skills (the spirit retains its own skills, however). A hybrid gains Immunity to Normal Weapons (p. 397, SR5) but loses the ability to assume an Astral Form (p. 394, SR5).
A perfect combination between spirit and vessel, the flesh form retains all of the vessel’s abilities, knowledge, and skills (except Conjuring skills), and its appearance is virtually indistinguishable from the original vessel. A flesh form gains the following powers: Aura Masking (p. 194), Dual-Natured (p. 395, SR5), Immunity to Normal Weapons (p. 397, SR5), and Realistic Form (p. 198).
2. What is the essence for a Hybrid or Flesh Form? Is the the spirit's plus the vessel? Just one or the other?
This one's a little trickier. The way I read this line from Street Grimoire, page 196 is that the original character is gone. That which makes them simply ceases to be - their body remains, which gives it some stats, but the Essence of the person is gone.
During merging, the vessel’s original spirit is consumed (if present) and that character is lost (though gamemasters may decide otherwise, if appropriate to their stories).
So I have been treating it as the Essence of the vessel is obliterated, and the spirit's Essence takes over.
3. A hybrid form can use cyberware, but can it get more (given the altered physiology)? Does the creatures new essence take the hit (meaning the potential for a LOT of cyberware)? Is any of this different for a Flesh form?
Another tricky question. I would argue that cyberware is incompatible with the spirit's Essence and therefore they cannot add more. This is as much a game balancing mechanic as it is my perspective on how Essence works. I would say the same for Flesh Form spirits too.
4. Randomly: Why is there no Spider Insect spirit?
As others have pointed out, spiders aren't actually insects. With that said, the
Aetherology book does cover the insect metaplane of the Invae (insect spirits). The metaplane is called Vhortas, or The Hive, and it exists somewhere near Azzorloth, the Bridge of Worlds. Either that or the Bridge simply gives access to Vhortas. There is a separate metaplane called Metabeles, or The Web, which houses all the arachnid spirits. This includes spiders, but also scorpions and similar critters. Based on the information in
Aetherology, the truly relevant portion that you'll want to look at describes the Warrior Plains and the Eater of Insects who rules the realm. It describes the war between the Invae and the Aranea, and can help fill in a few blanks. To summarize, the spiders are there, but they aren't interested in us. Instead, they want to wipe out the Invae, which might be part of the reason the Invae are invading our world. Also, the Invae metaplane has almost no resources left so there's that too.