CRJ-200 flight crew reported a flap malfunction on approach.

Narrative

Well on a visual approach into ZZZ airport; The flaps failed and became stuck in the 30 deg position. We executed a go around; received delay vectors to properly run the associated QRH; and then attempted a second visual approach to landing. While being vectored for the second approach; wind shear and moderate turbulence made it extremely difficult to maintain altitude and airspeed; and we suddenly gained a significant amount of airspeed and exceeded the flaps 30 limitation speed by a few kts. The Pilot Flying immediately corrected it. Also; while coming in bound on the approach; because we were concerned about our fuel on landing the pilot flying did not realize the gear was not yet extended until passing below 1500 ft. height above touchdown. Once the gear was selected down it did not fully extend until passing below 1000 ft. The gear was still verified to be down and green; and because of the time threat given by our fuel load both of us Pilots elected to continue the approach. A safe landing was made. Once on the ground; we were so focused on ensuring the flap failure was written up properly that the flap overspeed was omitted and not written up before leaving the airplane; as both the Pilot Flying and myself thought the flap failure write up would cover both.In regards to the flap over speed; significant wind shear and turbulent conditions made it arduous to maintain a proper airspeed. In regards to the landing gear not being selected down before 1500 ft.; both the Pilot Flying and myself were very task saturated focusing on flight path management and calculating fuel on landing. Once on the ground; task saturation and a misunderstanding of the write up that we were doing was also the cause that led us to omit the write up for the flap over speed.In the future; if this event or a similar one are to happen; I will be sure to always verify that the proper configurations are met before 1500 feet as I do on normal routine operations. If time permits I will be sure to run through normal checklists at least once after running emergency checklist to ensure all normal configuration items are met. I will also share to slow myself down once on the ground and verify that all individual events received their appropriate write up; and not assume that one write up will encompass multiple. In other words; I will take the more conservative action and ensure that more than one write up is done for multiple discrepancies when in doubt.