Is it necessary to connect all GND's and VCC's on a standalone board?

Only one marked Vcc but you need to connect both Vcc and Avcc together even if you are not using the analogue capabilities, it says so in the data sheet-

AVCC is the supply voltage pin for the A/D Converter, PC3:0, and ADC7:6. It should be externally connected to VCC, even if the ADC is not used. If the ADC is used, it should be connected to VCC through a low-pass filter. Note that PC6..4 use digital supply voltage, VCC

any other reason WHY than the datahseet says so? I would like to see some test results on that one

there are 2 ground pins physically connected

Ever thought why that is? Do you think the manufacturers do it for fun? It costs money to bond out a pin on a chip and they would save some if they did not do it. So where is the incentive?

It is because although the pins might look to be physically bonded there is:-

  1. A current carrying capability involved with any bonding wire, by using one wire you are halving that.
  2. There will be an impedance difference between the two bonds that could cause instability if only one is connected.

So yes it might function but it will not work like it is specified to.

Do I think its for fun? NO I think its cause they have to conform to a package specification and had X extra pins. and It apparently does not cost them that much to bond wires to a frame as the 328 in TQFP and MLF has 3 grounds, but yet the specs dont change.