Needing to install things is kind of the point of needing the laptop, so it makes perfect sense that they want to install Office, AV, and certificates. There are no surprises there. To do that, they need admin access, but I would want to revoke that access once they were done.
I would want to know the list of everything they want to install, and if they have central control over the AV (and if they do, why they want that).
If your worry is that they might install malware, then download a Live CD of an anti-malware program and run it on the laptop after they are done.
If the laptop is only used for school work, then there is really no harm here. If your child will be using it for other things, then there might be some privacy conflicts.