On modern rigs it is done internally (Trivial for the micro to offset a number before programming the synth), older stuff usually did not have the precision for it to matter (If you were +-10KHz, that was as good as the dial got).
Where to put the IF filter is something of a tradeoff as placing it immediately after the mixer means the IF amp is only exposed to the energy in the passband so overload is less of an issue, but while not an issue on HF, it does hurt the system noise figure on VHF and above.
Ideally you want to place a wide filter after the mixer (wide so it has good overload performance) followed by a little fixed gain to make up the losses followed by the main selectivity filters, followed by the main IF amp.
Note also that the mixer really should be wideband terminated on all ports, diplexers are your friends.
Yes, you should be paying attention to impedance matching (Quarts filters are normally hundreds of ohms, not 50, a simple L match will usually suffice....
73 Dan.