The thick line on a schematic is called a bus, it can be thought of as a bundle of separate wires that have similar function or go from one general area of a schematic to another. It is done purely for visual clarity, which may not seem intuitive if you don't know what it means but consider this. Say you have a 32 bit address bus on a microprocessor which connects to 10 other ICs. Imagine what it would look like if you tried to draw 32 separate wires in parallel, each connecting to all those ICs, you would have an absolute rat's nest that would be hard to follow. Instead you draw a thick line or in some cases a wide stripe and have the individual signals go in and out of that stripe, labeled where they enter and exit, the result is much more clear.
That's what's going on with the voltages, all of the power supply voltages here are drawn as a bus, with each wire identified by its label.
Schematics are not read in any particular direction, they are normally organized by functional blocks, often with little or no relation to the physical layout of the circuit. The schematic is there to describe the way the circuit works and group together components that are part of a certain function, like the power supply, the front panel buttons, the RF front end, and so on. Sometimes the parts of a subsection are physically clustered together but they could be spread all over the board if there were reasons for it to be done that way.