Happy New Year Boys...

That's a very dangerous circuit you've posted Dennis.

What you've got is Vdd at LIVE potential, and Vss is just -5v below it. You've put all your voltage drop in the NETURAL rail. That means your ENTIRE low-voltage PIC circuitry is actually referenced against your HIGH VOLTAGE LIVE. Yes it will work, but there is no margin for error anywhere, because GROUND is (more than) 250 volts away...

If you look at other half-wave rectified circuits (posted on this forum), you'll notice that Vss (0v) is sitting at NEUTRAL, with Vdd +5v above it (with all the voltage drop being done in the LIVE rail). So, in that instance most of your PIC circuit is close to GROUND (since NETURAL and GROUND 'should' be connected together somewhere along the Power Grid to your Wall Socket). This makes it a damn sight 'safer' if you really want to play with mains. I use the word 'safer' cautiously - because playing with supply mains for folks that don't know what they're doing is not safe at all.

All the above is negated by the fact that some countries Power Systems allow users to plug appliances in either way around.

Now I'm going to get serious here. Your questions highlight the fact that you don't know what you're doing and you're asking the forum for advice on values of components and such. Read the Datasheets for the components you're using and determine if what you are doing is correct for the purpose intended. For example, the TRIAC Datasheet should tell you what Gate current it requires (your R3 question) to switch on. Because if ANYONE gives advice on a particular component or value, and you end up killing yourself, the liability falls onto the person that gave you the advice.