Is it normal that a DAC outputs spikes?
The TI DAC8532 uses a Kelvin resistor-string (string of resistors that divide the reference voltage, with individual switches from the nodes to the output), so it is guaranteed to be monotonic. What you see does not sound normal, you must be writing zeros to it over the serial interface somehow. How did you implement the serial protocol?

The low-pass filter you put on the output is the reconstruction filter. It is used to reduce imaged frequency content (repeated frequency content above the Nyquist frequency). It's not always needed. The DAC has a built-in zero-order hold element that attenuates the images somewhat. If you are driving a system with low-pass frequency response, like a DC motor with a heavy mass attached, then you don't need the reconstruction filter.