At risk of asking a stupid question, have you got a copy of the Interpretation Guide?
It's essential reading if not!
For your specific queries:
4.16.2 - The IG does seem to imply that yes, you should inspect all vehicles.
There might be some room for not doing so for customer-provided vehicles, assuming that your contract of sale is sufficiently clear as to what responsibility sits where. For example, if you sell according to the EXW incoterm, the transfer of risk happens before the vehicle is loaded, so it demonstrably isn't your responsibility to inspect the vehicle as it is the customer rather than you that is loading it. This becomes more complex if you physically load the goods onto the vehicle though, as even if you're not contractually obligated to do so, practicality often dictates that it is necessary if e.g. a forklift is needed for the loading.
I could see auditors taking a different view on this though, so it's certainly not without risk as an approach.
There is no specific dispensation for couriers given in the standard.
In both cases though, the standard doesn't mandate a forensic level of inspection - for finished ambient product in suitable packaging, verifying suitable cleanliness/lack of strong odours could be accomplished fairly readily with a quick visual inspection?
4.16.5 - To an extent yes, as implied by 4.16.6 ("all the requirements specified in this section shall be clearly defined in the contract or terms and conditions and verified"), but you'd also be expected to have evidence of some areas as part of your approval of the transport providers, in order to satisfy the "and verified" element of this.
Worth noting that many couriers aren't willing to sign up to specific contracts beyond their own Ts&Cs though, so you'll need to consider how you manage that.
4.16.6 - You have the freedom to determine this to some extent, but you'll obviously need to ensure that your approach meets the requirements of 3.5.3. If your transport providers aren't certified, then you could start by downloading the audit checklist for the BRC Storage & Distribution standard and using that as the basis of your own audit template. It'll give you an idea of the things BRC wants to see in a transport provider, and you can always cut out any parts that are genuinely superfluous.