cap said:
I didn’t realize that Yavin was a gas giant. That’s a satisfying answer to that question.

Question #3: if Leia suspected that there was a homing beacon on the Falcon, why didn’t they go somewhere else and hire another ship to fly to Yavin? Did they want the Death Star to find their base?

That I can answer definetly. Leia is not the type of person to put innocent people at risk. Since the Empire was following the Falcon to the secret Rebel Base - which they were trying to find to begin with - they would have assumed that the first place that the Millennium Falcon lands WAS in fact the Rebel Base. One person had asked me, "why didn't they go to Cloud City and have Lando's people remove the homing beacon?" Well, it's obvious as seen in TESB what would happen if the Empire tracked them to Bespin, so if they went there instead of Yavin IV, then odds are Imperial Troops would storm Cloud City and hold everyone hostage. So it was right thing to simply go straight to the hidden Rebel Base, analyze the data stored inside R2, formed a plan of attack and engaged in a full assault against the Death Star.

Another question of similarity brought up was, "if Leia know that the Falcon was being tracked, wouldn't she have tried to find and disarm the homing beacon?" Again, another simple answer: Han Solo would not allow anyone to mess with his ship in anyway for whatever reason.