The error message that macOS/OS X supplies is the key:
the Wi-Fi symbol in the top right has a cross through it and when i
click it says "Wi-Fi: No hardware installed"
It simply cannot find it to configure it. Unfortunately, there's not a VRAM or setting file that will fix a failed board. An SMC reset won't have any effect because it's connected via the PCI bus which means if the SMC was failing, pretty much everything else on your MBP would be failing; the SMC controls power delivery to the whole PCI bus, not just individual parts.
The good news is that its fairly inexpensive and something you can repair yourself (Apple PN# 661-5867)
Ifixit.com has an excellent step-by-step tutorial with pictures that walk you through the replacement. They even sell the plastic spudger tools shown in the example. With a little patience and time, you can fix this without having to incur massive costs from a repair shop.
As for your Ethernet, that's technically a completely different issue; it's different hardware altogether but still part of the PCI bus (this is why SMC reset has no effect). When the OS reports back that it's "connected" it's saying that it has "found and made a connection."
To verify this, type
ifconfig en0 and you should get something similar to this (your's will have different values):
en0: flags=8963<UP,BROADCAST,SMART,RUNNING,PROMISC,SIMPLEX,MULTICAST> mtu 1500
inet 192.168.1.13 netmask 0xffffff00 broadcast 192.168.1.255
media: autoselect (1000baseT <full-duplex,flow-control,energy-efficient-ethernet>)
The important value here is
inet. If you don't get a valid IP address, it just means that DHCP didn't assign you one. A reboot will usually fix the issue.