We would love to offer some assistance and would be to lose you! The S4 is an awesome device and we want you to be fully satisfied with it!
In regards to the WiFi calling dropping, devices that use IMS Wi-Fi calling do not support a handoff to/from Wi-Fi & GSM, so leaving the radius of the Wi-Fi coverage can result in dropped calls. However, you specifically mentioned this happens within range of the router, so that adds another factor; you may want to try testing results on the other Wi-Fi calling preferences.
The one thing the 3 issues you've mentioned have in common is software, ultimately we would recommend a master reset to see if that reloads the software in a manner that corrects the things you've noticed. Android is highly driven on software and applications, it is not uncommon for an application to cause corruption to the software. Reset: Samsung Galaxy S 4
So... I've determined that the issue was my Fios router and have purchased a Netgear N600 and have had success since upgrading to a Wireless N router.
What's odd though is that I never had this problem with the Galaxy S2. Does the Galaxy S2 use IMS Wi-Fi calling or a different type of wifi calling? I'm curious if there are different types that would allow for that transition to cellular from wifi when the wifi signal weakens or drops.
I've decided to keep the Galaxy S4 despite the software defects I mentioned (unable to answer a call when on the phone already and random setting changes).