If your phone (for example, an iPhone) gets seized by the police, do they have sufficient technology to copy sim card (or any data) even if you cancel you provider and put phone in lost mode? If so, is there any way to remotely wipe sim and/or data on said phone?
No you can not. On the other hand, with iOS 11.4 it will be possible to limit what a third party can do to your phone as the Lightning USB connection will go into restricted mode if you don’t use the phone for a day.
Regarding your SIM: the data on it and the access it provides is trivial to get from the phone company. If they were interested in getting SMS messages or cloning your subscription, it would be much easier to just call the provider.
I think there is a misunderstanding in the concepts. If your friend is using an iPhone, there will be very little data in the sim card. It basically would only allow to use that number. It may contain sms and addressbook info, but on a smartphone, you most probably are storing this data on the phone itself.*
The sim is only giving usage of this number. This is not trivial in itself, as it could allow the seizing actor to receive your calls and sms, and could be enough for triggering password resets on other services (your should use recovery/second factor systems not tied to his phone number). However, that's already available to the telephone company, which could issue a new sim linked to the same number (or the calls/messages to your number could be rerouted through several ways). Obviously, once you cancel it, that sim gets useless.
Note 1: You could store that data in the sim if you really want, but it's quite unusual.
Note 2: There may be old data in the sim, before your friend started using this smartphone. As it is unused (transfer them to the terminal if it wasn't already done), they can be deleted in advance, so there is nothing there when seized.
As far as I am aware they can't (legally) access your sim unless you give them the Pin details. If your sim doesn't have a password (different than phone password) then they can just put it in another phone. It is technically possible to crack a sim/puk number:
But it is very hard to do just looking at the above. Not this is from 2014, so possible is that more advance cracking software exists AND that this exploit is been patched. So if I were to gable I would say access to your phone is safe.
However, finger authentication is different. Its covered under different laws and they can legally force you to unlock it or just lift a fingerprint and open it. So if your mate is doing illegal things I would suggest that he doesn't have finger authentication.