Resistor / Capacitor on digital signal
There are a couple of different things going on.

1) Series resistors on serial communication systems are generally a part of a larger problem known as "signal integrity analysis" and "electrical termination".

In the case of SPI the most relevant line to need a "termination" is SCK.  Why does a slow line like SCK need termination?  The issue is that while the SCK bus frequency is generally MHz the edge of that signal may have Gigahertz components from modern transistor technology.  And modern transistors receiving that signal may also be able to respond at Gigahertz rates.

So, you get a launched signal, a transmission line, a reflection or two on the line, and you may get a double-clock event on SCK.  Not good.

Simply adding a resistor in series damps those reflections as well as limits the amount of current that can cause a reflection.  The precise amount of resistance generally isn't too relevant at single digit MHz speeds.

2) If all your SPI signals have resistors, are the packages of the communicating chips something like QFN or BGA?  For a package like a QFN, it can be really hard to probe specific signals so bringing them to resistors which can be soldered or probed can help.

3) Sometimes the series resistors are there to help out with ESD protection.  I suspect that's what R4/R5 are meant to do in your circuit above.  They could be to help signal integrity, but on such a small board they're probably not relevant for that.

4) The C5/R3 combination is serving as a high-pass filter so that DTR only sees the edge changes on the RESET line--and, in this instance, only rising edges since the resistor, by default, discharges to ground over time.