Welcome to the forum and iSS. Phone shops are a little different than others, but not by much. Here's the scoop:
No, you can use any phone you like. I can't tell you or guide you on that one.
Next, most of the calls made DO NOT use a call app because they must be recorded. There is a special phone number contained within the shop instructions, once you are assigned a phone shop, that you will use to make the call. If you call using the CALL button in the mobile iSS app, it won't record the call. Also, you cannot use any other call or phone apps.
Once the call is recorded, you will be able to listen to it before you submit your shop report. It will be attached to the report automatically. You can't change or delete it, or it will invalidate the shop and get it declined.
Hope this tidbit of information helps.
One last tidbit: Consider using Google Voice. It is a system and method where by you are assigned a phone number and voicemail different from your own, and it get attached to the phone you are using. If you do multiple phone shops, this is a great asset. Check out other discussions on this forum for more information, and also Google. If you do not have Google, then you would need to sign up, but it's a "phone" for thought? Ha.
Happy phony shopping.