Arp Beat Sync quantizes your performance from the keyboard so each note you play conforms to a clock reference, be it the internal clock of the instrument, or external MIDI clock.
With Arp Beat Sync enabled, and the synth syncing to its internal clock, the first depressed key will not trigger until the master clock gets back around to "the 1”, depending on the selected clock division. This is how you can be sure that you're quantized properly. The "1" is denoted visually by the blink of the tap temp LED.
When Arp Beat Sync is enabled and you are slaved to external clock, the arp will quantize the the MIDI clock tic that is received concurrently with a MIDI Start command.
Regarding the Sustain Arp global options, these control how an attached sustain pedal affects the synth when the arpeggiator is enabled. Arp Hold and Arp Hold Momentary basically act as a foot control for the HOLD button, allowing you to use both hands for playing/tweaking, rather than having to manually press the HOLD button. The former latches the HOLD button, while the latter engages it only while the pedal is depressed. The Sustain option works just like a sustain pedal normally does, where while the pedal is depressed, the envelopes for all triggered voices are held at their Sustain stage.
I hope this helps!