The person Bequeathing someone needs to be a Keyblade Master or someone on the level of a Keyblade Master, and the person being Bequeathed needs to have a strong heart. All you need to wield a Keyblade is a strong heart. In order to obtain a Keyblade though, you need to be Bequeathed. Terra Bequeathed Riku in Birth by Sleep. So, as stated above, that caused a Keyblade to choose Riku. That Keyblade was Kingdom Key. In KH1, during the storm on Destiny Islands, Sora unknowingly touched Riku's heart. During that moment, Kingdom Key saw Sora's heart as stronger than Riku's since Riku was falling to darkness and chose Sora instead and jumped over to him. Sora is able to wield it because he has a strong heart. So, Sora receiving a Keyblade is a rare and unique case since he wasn't Bequeathed. He happened to be at the right place at the right time and happened to have a strong enough heart. Later, at Hollow Bastion, Riku took back Kingdom Key because it was still technically his/he showed that his heart was stronger than Sora's during that moment. But, after Sora gave his iconic speech, Kingdom Key chose Sora again since Sora proved his heart was stronger than Riku's, and this time, it was permanent.
And jump to KH2, and Riku now has another Keyblade called Way to the Dawn. It resembles Soul Eater. Soul Eater isn't the same thing as Way to the Dawn. Soul Eater is just a sword. He can still summon Soul Eater separately from Way to the Dawn. It's unknown how Riku got Way to the Dawn. It's unknown what happens when someone who was Bequeathed loses their Keyblade. So, it's possible that when someone who was Bequeathed loses their Keyblade, another Keyblade chooses them. So, it's a possibility that after Riku lost Kingdom Key, Way to the Dawn chose him. Who knows though. We don't know for sure how Riku got Way to the Dawn and we don't know for sure how Riku got Destiny's Embrace. There are many theories though.
TL;DR: We don't know how exactly Riku obtained Way to the Dawn.
And falling to darkness isn't what leads you to lose your Keyblade. When Riku was falling to darkness and Sora touched Riku's heart, Kingdom Key saw Sora's heart's as stronger and chose him instead. Riku losing his Keyblade is a combination of him falling to darkness and another person who's heart is stronger than his touching his heart at the moment of him falling to darkness. It wasn't just simply because he fell to darkness.