1 What kind of short circuit protection does a basic function gen have a? Example what happens if I have a capacitor between my voltage rail and ground. My theory is that when I increase the frequency the reluctance of the capacitor will go down and act like a short circuit. Will this break my function gen? To answer this you have to look at generator manual. Most lab grade generators have protection.
As far as C goes depends on the C. Most C's have a rising Z characteristic past a certain point
due to internal parasitic L.
2 How do you normally fit the impedance of the circuit to match the 50 ohms? In my understanding the impedance will change according to the frequency that’s fed in to the circuit.The generator sources 50 ohms via circuit design, same is true for load.
There are many methods to Z match load to source,
http://electronicdesign.com/communications/back-basics-impedance-matching-part-1If you are working with LF types of applications, audio for example, Z matching not considered
an issue if load is high Z. That will impact generator Vout.
3 Should I keep something else important in my mid while I am experimenting with my new function gen so I won’t blow it up?Have on hand attenuator pads and start with a 20 db pad when applying fgen to circuit,
that will protect you in almost all applications where voltages and power levels are small
signal based. fgens and scopes on 50 ohms get toasted often because power is exceeded.
If you have a load that can source power use a pad. Note the manual usually discusses
operator safety for the fgen, methods and approaches.
http://cp.literature.agilent.com/litweb/pdf/5989-8790EN.pdfRegards, Dana.