1. I recently heard that Trezor had some security vulnerability exposed (with its recovery seed, I believe). What happened there, and is this a danger for the future?
The vulnerability required physical access to the device and destruction of the casing, so it would only occur if someone stole your Trezor. The vulnerability has also been patched with a firmware update (for older devices) and a bootloader update (for new devices; the bootloader cannot be updated outside of the factory).
2. Once my device arrives, I want to test the recovery seed (pretend I lost my device, and use the recovery seed to recover my wallet). As I understand, if I do this with the Ledger, the seed and thus my device will be worthless afterwards; whereas with the Trezor this is possible without problems. Correct?
No, where did you hear that? You can restore your recovery seed without any risk or damage to the device. They are designed for people to be able to restore seeds and then wipe them later to allow for people to recover coins from lost devices.