@Capricorn12 

Happy holidays !

1) Can I use the ax6000 as my primary router and connect the Unifi AP Pro to get greater wi-fi coverage and signal strength in the basement and the garage?

Yes.

2) If so, can I maintain the w-ifi active on my primary router?

Yes.

3) Do I have to create separate SSIDs or can I have the same one for the router and the AP Pro?

It's your decision - there's no difference. You can have them the same or different.

4) Is there a possibility of signal conflict?

Yes, but only if they are closer enough - there could be a wireless interference. (I doubt that in your case).

5) Is there a tutorial that exist on to program both devices for such configuration?

There's nothing special here - it's the same case as with your previous Synology router.

AX6000 LAN port => Unifi AP Pro Main/48V (Unifi powered by the power adapter included).

  @Capricorn12 

1) From my router to the Bix box (junction box) I have and old Category 5 cable (20 feet long) which I believe is limited to 100 mbps, and from the Bix box to the UniFi AC AP Pro, it's a Category 6 cable (45 feet long). Is there a possibility that I might have transmission restriction (1 GBs from the Lan port) to the UniFi AC AP Pro unit?

Yes, there could be a bandwidth limitation, because of the old Category 5 cable - it's advisable to use Category 5E / 6 to ensure a gigabit connection to your Unifi AP Pro.

You could determine that very easy from the AX6000 WebGUI (just check the negotiated speed on the port where the Unifi AP Pro is connected):

2) As for the Unifi AC AP Pro unit, is there any specific features or program functions that I have to: turn off or on? Parameters to modify? Other?

It should be similar as when you've used your previous Synology router. Maybe only changing the wireless channels for 2.4 & 5GHz to be different, so you can avoid a potential wireless interference between the AP and the AX6000.