No. Price has almost very little to do with reception and more to do with the general finish of the product. It used to mean more features too but there’s a rather pronounced bell curve on that aspect these days. If you’ve got a specific device in mind, GSMArena should be able to give you all the information you need.

Reception is dependent on which bands the phone supports, and which bands your sim contract supports. You can get cheap phones that support all major bands, and the rest is up to the sim

It could, but realistically not much in most cases. Only if you’re on the very edge of losing a signal entirely.

The specific network chip and device antenna design could play a significant part on reception, but realistically there won’t be much of a difference in the real world, lots of research and development has already gone into the technologies we use now.

Higher end phones will often support more frequency bands, and thus support more signals, but no carrier uses all of them. Just make sure the phone you pick supports the bands your carrier uses.

Now when new technologies come out, that’s when you can see real world significant differences between devices because there isn’t as much real world experience with a new technology yet, but everything out now and in the near future has already gone through that phase.

Removed by mod

In general, devices with plastic cases typically have better reception because plastic is RF transparent. Devices with metal cases tend to have worse because they block RF. That’s grossly simplified but it’ll get you started on researching it.