Electronic – Rotate Board and Components in Altium

1. VCC and GND routing

Best way to deal with the GND routing is using Polygon Pour. (Related question on this site.) In Tools \$\rightarrow\$ Polygon Pours \$\rightarrow\$ Polygon Manager click on Create New Polygon From... \$\rightarrow\$ Board Outline

You can prefrom this action on all layers one by one, but do not forget to connect these GND pours.

As for the VCC routing it is OK as you did on your second picture. If you want to use separate VCC plane you will have to use vias to make connection between the component plane and the VCC plane.

2. Trace widths

It is recommended to use wider traces when dealing with higher currents. There are a lot of online trace width calculators (like this and this) to determine the required trace width. (If these tools are too compicated for you, I was told to use min. 1 mm (80 mil) / 1 A as a rough rule of thumb but maybe it is a bit of exaggeration).

3. Routing using multiple layers

If you could not manage the routing without using vias you have to rearrange your components either to avoid the using of vias or to make enough space for them.
Below a part of my first PCB which I have routed manually. I used 7 vias to make the highlighted route. It was one of the last remaining route and it was quite crowded there but I could find a way to connect the pads. Some may say it is not a nice track, maybe it is not. But it is good for showing that sometimes you can find place for vias, especially when you do not want to spend another day to reroute the whole PCB.

You asked for another way, Auto-Routing could be one. I prefer routing manually and I recommend you to do as well, it is reliable I think. But I must say that it is an option too. Maybe it could do the whole routing for you, maybe just a small part and you have to finish/fix the rest manually.

4. Drag component with connected tracks

To enable this option go to PCB Editor - General page of the Preferences dialog (Tools \$\rightarrow\$ Preferences). And select Connected Tracks from the Comp Drag list.

After you set this you can drag and move componenets with the connected tracks by the Edit \$\rightarrow\$ Move \$\rightarrow\$ Drag command.
Note: when using this command and the Comp Drag mode is set to Connected Tracks, the rotate, flip and TAB key commands are unavailable.

Going to make a guess on this one. In the schematic you can simply select a part and hit the spacebar and it rotates. In the PCB editor the part has to be "floating" in order to rotate it, meaning you have to click and hold it (as if to drag) with the mouse, and then hit the spacebar while "holding" it. The same goes for flipping the component (X-Y), etc.