Relay Controlled Light Circuit Help
What you're trying to do is fine. But consider using an AC-load Solid-State Relay (SSR) instead. They will draw little load current from your 5 V to power and have no moving contacts to arc.

You can find plenty about them on the interweb. But in short, they come in DC-load and AC-load versions and the later is a convenient little package containing a triac to switch the mains and controlled by an opto-isolator. You put a control voltage into the SSR, the internal IRLED lights up, the triac's turned on and your AC conducts. You can get zero-crossing versions, whereby the output is only turned on or off when the AC mains voltage crosses zero, avoiding the spike of current of a load switched on/off as the mains wave is high.

You'd want a device for a 264 V (240 V + 10%) or higher load voltage at 1 A or higher. Fuse the supply for the current rating of your SSR. You can get SSRs in little 8-pin packages up to inch-or-two potted through-hole packages or huge ones with screw terminals, with the cost rocketing as you go. Avoid the DIL ones, the pin gap's not good enough for my liking or your home assembly. Go for a device in a larger package, something like the Panasonic AQG22105J.

Incidentally, I have yet to see one of these larger devices that needs a series resistor on its control voltage input - they just take the control voltage. But that's not much use if it does, so if you pick a different device to the AQG22105J, check that on the datasheet like everything else.

Answering your other questions:

(1) The switch should break the LIVE wire, not NEUTRAL, so that a switched off lamp has no power going to it.

(2) Look at SSRs, as above.

(3) Most likely don't need R if you use an SSR but check its datasheet. Otherwise just your switches and USB-derived 5 V power on the 5 V side.