Sure, a giant spider can be a mount.
Here is what the Player's Handbook says about the eligibility of a mount in the Mounted Combat section (p. 198):
A willing creature that is at least one size larger than you and that has an appropriate anatomy can serve as a mount.
The giant spider is Large size, and humanoids are Medium size, so the size restriction is met.
The wildshaped druid is supposedly willing, so the willingness restriction is met.
If the DM rules that a spider's anatomy is appropriate (I would), then the anatomy restriction is met, although a DM might rule otherwise.
As long as you have the support of the DM, then yes the wildshaped druid can act as a mount.
Anything beyond that is up to the DM.
There are no rules for multiple creatures riding a single mount. The rules for Mounted Combat heavily imply a single rider per mount by omission of any rules about multiple riders, but there's nothing that explicitly prohibits it. So, the DM could allow multiple riders, but they would have to create their own rulings, because the rules are silent.