Trace the blue and yellow,are they connected to anything else before reaching the relay?

Cisco there are three equally important components-quality HVAC, the install by dealer, and probably the most overlooked and disregarded is the ductwork system. these are my minimum specs for a new HP system. both outside and inside units should be replaced to have a properly matched system. 15 SEER, 12.5+ EER, 9 HSPF best matching VS air handler full BTUs in both cooling and heating for your rated size R-410a refrigerant(same as Puron) scroll compressor preferred electronic demand defrost preferred thermostat with "dehumidify on demand" feature staged backup heat strips new and correctly sized refrigerant lineset you want a thorough inspection of your ductwork system. size, overall condition, supply and return lines, insulation qualities, leak test, etc. any hot/cold spot issues in your home should be addressed. I would only use authorized dealers for the various brands that provide quotes. see mfg websites. I would look at Trane/AmStd,Rheem/Rudd,Carrier/Bryant. Depending on your location, I would not purchase a new HP system that did not have electronic demand defrost. IMO

All these systems are comparable. I don't think I'd splurge the $2000 to get the 15 SEER system unless rebates made it worth it, and in this case they don't appear to. You don't pay utilities, and between the Carrier products, you don't gain that much in way of features or reliability per se. You weren't quoted a "genuine" Amana unit. These units have model numbers starting with "A." They are considered a more premium unit in line with Carrier, for instance. However in comparing Goodman's base equipment with Carrier's base equipment, I don't see an advantage either way if all are from the same reputable installer. The installer will make the difference. Personally if I were looking to install a base grade model, I would look at Trane's XB line. For a builder model, I think they are pretty solid. Also more expensive. Or consider looking one step up in Carrier and Amana lines at the Carrier 25HCB360 or Amana ASZ14060.

I personally have no problem with a customer following me around. I prefer to educate them on certain items they can do themselves. A little communication goes a long way to make a user feel warm and fuzzy as long as they don't get in the way. I have clients that only need me or one of my techs. to come around every 3 years or so to do real maintenance and checks. The residential maintenance agreements do help me keep technicians busy during gaps in the schedules. I actually have clients who want someone to come out and change their filters. Most are elderly or afraid to touch anything. We usually try to schedule those when a tech. is going to be passing by and we can do it gratis if the customer provides the filter. It's amazing how that "value added" service has helped business. But as you can see, for some people those maintenance agreements are worthwhile to some while others can save their money and do certain things themselves. Of course, for commercial clients, it's cheaper for them to buy an agreement than it is to hire someone full time to do it. And what's great is they can call the shop, ask questions and if the office Administrator can't answer a question (she does great), a tech. will call back. Even many handy types buy the agreement just to have resources (we also sell parts). These extras have allowed me to pretty much lock in whole neighborhoods.