Thermostat wiring: heat and fan of but AC not cooling & 2 disconnected wires!
It's fine that the orange and yellow are not connected; this assumes they are not connected to anything inside the furnace.
Running 7 wires for a thermostat is normal for future enhancement of either your HVAC system or the thermostat itself. The additional benefit of running too many wires is that if there is a faulty or broken wire like red then you can just repurpose a different color without running a brand new t-stat wire. If you only ran 5-wire and red turned out to be faulty then you need to run a whole new wire; hopefully 7-wire this time ;-)
Yes, there are generally accepted colors for stuff but there's nothing physically wrong with using &quot;wrong&quot; colors as long as they land in the correct terminals at both ends of the wire.
You'll notice there's some gray tape on the blue wire which is a standard wire color for cooling in an A/C unit. The yellow should have been used but whatever.
The only way to truly know which wires go where is to read the manuals: thermostat, furnace, and A/C unit. G needs to land on G at both ends of the wire regardless of wire color.
To me everything looks fine here. You need to add pictures of the wiring inside the furnace and in the A/C unit. If you're not able/willing to do this then you need to call a professional.