There is no web-based GUI to operate the receiver's entertainment functions (playback from sources, volume, input selection, etc). There is a web-based GUI that you get if you type in the unit's LAN IP address, but it only controls a few configuration settings you'll almost never care about. The only way to control the unit over the network for entertainment is to use one of the mobile apps.
No. Compare for example to the Denon AVR-E400 which is a 7.1 receiver, where you have the option of running it in 5.1 mode, plus having a pair of "Assignable" outputs which you can use to power your "Zone 2" speakers -- in other words you could use the E400 to run 5 speakers plus a powered subwoofer inside the house, and then use the other two "assignable" outputs, instead of using them for 7.1 "Surround Back L+R" you use them for your stereo outdoor L+R speakers. Being able to use two outputs of a 7.1 receiver to instead power a remote pair of loudspeakers is a common feature of 7.1 receivers, but not of 5.1 receivers like the E300.
Yes, you can hook up a turntable to this unit. It has left and right channel audio inputs that are assignable. However these are not phono inputs which means you might need a phono pre-amp connected between the Denon E300 and your turntable.
The receiver has only a wired Ethernet port, but there are two ways to not have to run an Ethernet cable all the way to the router. You can easily buy a cheap wifi bridge that would plug into the Ethernet port and provide an antenna to connect to your wireless network with no drivers needed (Many cheap/used wifi routers can also be put into bridge mode to serve the same purpose). I am using powerline networking to carry the network from the router into the nearest power outlet, and then out of the power outlet by the home entertainment cabinet to a switch that serves all components that need Internet.
This receiver has a line level output for the subwoofer, so you will need an active subwoofer or an amplifier for the subwoofer. There are a lot of controls in the software including bandpass filter type, crossover frequency and level. It will also roll off the low frequencies of your high pass speakers if you select that function.
I used half of an inexpensive RCA cable that was in a drawer. It was probably a cable that came with something I had purchased. I connected it between the subwoofer output of the receiver and the input of the subwoofer amplifier. I will replace this cable with a higher quality RCA cable later. I still have some tweaking of the system but for now the system sounds great.
I would recommend purchasing a good quality cable and a well shielded one if the length is much more than a meter, but no need to look for a special subwoofer cable. If a cable will carry a full bandwidth signal it can handle a subwoofer with no problem, and you won't do any damage if you use any RCA to RCA cable that is in good working order.