■ On approach we received a GEAR DISAGREE warning message with the right main landing gear showing not down. At this point the Captain notified Tower that we needed to break off the approach and run a checklist. I was the Pilot Flying, so the Captain ran the QRH. As he went through [the QRH procedure], he got to the point of pulling the manual release handle. At this point I asked him if I could take a look at [the procedure] first to make sure we were not missing anything. I read in the notations about cycling the gear and stated my desire to cycle the gear. He stated that he’d either seen this in the simulator or heard of other guys cycling the gear, and that it had exacerbated the problem. He continued with the checklist and pulled the handle, but the gear still wouldn’t come down. He notified Company and talked to the passengers and Flight Attendant while I flew and spoke with ATC. The checklist took us to the point of Gear Up/Unsafe Landing.

We flew over the Tower at 2,500 feet so ATC and CFR (Crash Fire Rescue) could take a look at the gear and confirm it was up. They confirmed it was up, so we prepared for a gear up landing and notified Company of our intentions to land gear up.

■ [We] departed…with the intention to land in Houston (IAH).… The weather in IAH was good with possible pop-up thunderstorms in the area, which gave us Dallas (DFW) as an alternate.… We originally had 10.1 [calculated fuel remaining at IAH], with a scheduled 3.6 burn to DFW. As we started the…arrival [to IAH] from the northeast, we were given a reroute…from the southeast.… The CA (Captain) informed Dispatch of our situation. [They]…replied…that no holding was happening and that everyone was still getting in. This brought our fuel down to approximately 8.4 in IAH.… We felt comfortable continuing…and were given vectors to the north for Runway 8L, which included multiple vectors around heavy buildups. On downwind for Runway 8L, we were informed that an aircraft went around from Runway 8R for windshear, and during the turn to base leg, the radar was showing solid red moving north toward…Runway 8L. We made the decision to divert…to DFW.… [Enroute to DFW] the CA notified…Center…that we were minimum fuel, as our EFOB (Estimated Fuel Onboard) [at DFW] was indicating 3.4 to 3.6.… We did have to deviate around several cells between IAH and DFW and were given several delay vectors by Approach as we continued to alert them of our…fuel status. Weather in DFW was VFR.

We were given headings and altitudes that eventually put us on the glide path to Runway 17C, which did have a displaced threshold to 8,125 feet. I did verbalize around 1,600 to 1,800 feet that I had the PAPIs, and they were indicating 2 white and 2 red. The Captain suggested I follow the magenta dot so that we would be as close to the front part of the TDZ (Touchdown Zone) as possible, even though we were in [VMC]. All callouts were made, even the 500 feet “STABLE” [callout]. At this point [we] were low,…4 red [PAPIs], and before I could state my intentions to level off and catch up on the PAPIs, Tower [directed a] go-around.

■ Boeing Field (BFI) ATIS was broadcasting VMC…and was advertising the ILS to Runway 14R. We were expecting a visual approach. When ATC cleared us for the visual approach, they specified the Harbor Visual approach procedure without a proper heads-up. We quickly reviewed and briefed the Harbor Visual approach while trying to descend.… We received a TA due to VFR [traffic beneath us] crossing our path on final, which further prevented an effective descent.… We were between 800 to 1,200 feet and outside of the stabilized approach parameters and decided to go around. We advised Tower that we were going around. We anticipated receiving instructions from the Tower Controller, but he stated to fly the published missed approach procedure. Knowing that the Harbor Visual approach did not have a published missed approach procedure, we assumed he was referring to the ILS 14R missed approach procedure.

While the Pilot Monitoring was switching the iPad to the ILS Runway 14R procedure, Tower pointed out a Boeing 777 in close proximity on approach to Sea-Tac Airport, which we had in sight.… Our paths were converging over the top of BFI airport.

■ We transferred controls so the Captain could do the landing. We burned down to 1,000 pounds and were returning to land when we received an ACARS from Company saying to cycle the gear. I asked the Captain if he wanted me to, and he said, “Yes.” I pulled the gear handle up and got three white up lights, then pulled the gear handle down and got three green downs. We notified the passengers and [told] Tower we had all good indications but to have CFR standing by just in case. We landed, stopped on the runway, and notified everyone that we were okay and able to taxi to the gate.

■ We went around.… To say we were nervous watching the fuel go to 2,000 pounds was an understatement.… The CA [advised ATC] and we asked for Runway 17L. We spent minimal time in the air up to 3,000 feet and back in the pattern.… I asked [the CA] if he felt more comfortable flying this approach.… Initially he said, “No,” but while on downwind changed his mind, and we transferred controls.… As we crossed the threshold, I noted…2,000 pounds; by the time we pulled off the runway, it was closer to 1,920. Taxi to the gate was uneventful.

■ To avoid the Boeing 777 and its wake turbulence, we kept our altitude at 1,500 feet and slightly shifted course to the right to avoid passing directly under the Boeing 777’s flight path. [Its] altitude appeared to be 400 to 500 feet above us.… Descending off to our left, the Boeing 777’s altitude would have been 1,900 feet over the top of BFI if [it] was on the glideslope. At about this time the Pilot Monitoring confirmed that the missed approach procedure was to level off at 1,500 feet and fly along the localizer course.

At this time the Boeing 777 appeared to be descending through our altitude, and we were in imminent danger of the aircraft’s wake turbulence. The best course of action was to alter course slightly to the right. At the same time the Tower Controller stressed that we could not turn towards Sea-Tac Airport and needed to fly the published missed approach procedure, which was now slightly to our left. By the time the radio transmission was completed, we were…able to safely return to the ILS 14R missed approach…course, knowing that the Boeing 777 was passing through our altitude.… About that time,…we felt some of the wake turbulence from the Boeing 777 that we were trying to avoid. The Tower Controller handed us over to Approach Control, [who] gave us headings and vectors back to an uneventful approach and landing to 14R.