How many miles on the car? most FWD vehicles have factory-recommended replacement of CV-Axles/drive-axles/halfshafts every 60k miles. My 94 camry is recommended every 30 (but seeing as how I drive a 94, i obviously don’t have the money to do it that often, I get by on 60k replacements lol)
-The joints in these could be worn out in such a way that they only click when starting from a certain position rotationally-speaking. If you can, get under the car safely (either a lift or jack it up and put it on stands as crawling under a civic would allow less-than-ample workroom 😛 ) and see if they have any play in them either radially or laterally. If so i’d suspect these or a related component like hub bearings which causes something to be able to shift when power/torque is applied.
-If those check out ok, check for lateral play in your front wheels, should be none ideally. Grab the tire at 9 and 3 and push/pull opposite directions (like you are turning the steering wheel, axis-wise) See if that allows you to recreate the sound. (IMO less likely a cause of the sound but quite possibly a reason for instability over bumps) If that makes the same noise, it’s likely your steering end-links (another commonly worn out part)
-My final thought on the matter, which could link both of the symptoms you describe, is worn shocks/struts or mounts/bearings (however yours are setup, i’m not familiar with hondas). Raise the vehicle and secure it with jack-stands, remove the wheels for easier access, and see if you get any play in the shocks/struts in any direction (although i’m thinking if this is the cause, you should be able to recreate the sound by getting play laterally in the shock in the fore/aft direction with the car.
Hopefully at least some of this was helpful. Good luck and be safe.