Welcome to the dark side, cool bass! I'm not a luthier, I don't play an EUB, and I don't know all that much about Baby Basses specifically, so please take this with a giant shaker full of salt.
1. Do these have truss rods?
Nope. Necks on the big girls are much more sturdy, so it's not necessarily necessary. The baby bass is strange and has a neck angle adjustment and the tailpiece on these can be adjusted too. Most DB don't have those adjustments. Use with caution - little changes can just ruin your tone.
Adjusters on the (floating) bridge raise or lower action for most DB, including this one. Action will be sky-high as compared to a BG and every adjustment makes a big difference in feel and tone. As close as we have to a truss rod is the soundpost which is a rod of spruce that is friction mounted between the back and front, a little below the bridge, off to one side. I don't think the baby bass has one of those.
2. Are they prone to dead spots?
Not really, but not never. Since your fingers are much more interactive with the string and fingerboard, you can feel a lot of that. It's nothing like a dead spot on a BG - you can fix it with technique while playing. Places that sound funny in whatever way will need to be fixed at the luthier. There are other things like wolf tones and tailpiece buzz and stuff to take the place of your worries about dead spots.
Yeah. Not often (again, they're way thicker than a BG), but it does happen. However, it's not a thing - often the FB can be planed to compensate and you might not even notice.
DB are traditionally wooden, although the baby bass is a rare bird in the "traditional" respect. Luthier-type-micro-woodworking skills are needed to screw around with mine. I can do almost no setup on DB. Everything goes to the shop. Good part is that it only has to happen every decade or two versus every month or two on my Ibby (on which I can do almost everything).
Also, please remember that EVERYTHING costs more and takes longer on the big girls.
