It is believed that most gods including Odin, Thor, and multiple other gods and goddesses die at the end of Ragnarok.
Yes. Heimdall and Loki slay one another.
From the Prose Edda by Snorri Sturlson in the Gylfaginning Ch 16, emphasis mine:
The Wolf shall swallow Odin; that shall be his ending But straight thereafter shall Vídarr stride forth and set one foot upon the lower jaw of the Wolf: on that foot he has the shoe, materials for which have been gathering throughout all time. (They are the scraps of leather which men cut out: of their shoes at toe or heel; therefore he who desires in his heart to come to the Æsir's help should cast those scraps away.) With one hand he shall seize the Wolf's upper jaw and tear his gullet asunder; and that is the death of the Wolf. Loki shall have battle with Heimdallr, and each be the slayer of the other. Then straightway shall Surtr cast fire over the earth and burn all the world; so is said in Völuspá:
Different translation here:
The wolf swallows Odin, and thus causes his death; but Vidar immediately turns and rushes at the wolf, placing one foot on his nether jaw. On this foot he has the shoe for which materials have been gathering through all ages, namely, the strips of leather which men cut off for the toes and heels of shoes; wherefore he who wishes to render assistance to the asas must cast these strips away. With one hand Vidar seizes the upper jaw of the wolf, and thus rends asunder his mouth. Thus the wolf perishes. Loke fights with Heimdal, and they kill each other. Thereupon Surt flings fire over the earth and burns up all the world. Thus it is said in the Vala’s Prophecy.
According to Snorri's texts, yes, but it is the only source of such a story. He says:
"Loki á orrostu við Heimdall, ok verðr hvárr annars bani."
My own translation: "Loki goes to battle against Heimdallr, and both cause death to each other."
We don't know how much we can trust on Snorri's texts, since they were written long after the old norse traditions were dead, thus it is impossible to know if the earlier scandinavian people believed it, but it adds some symetry to the whole "one kills another" thing.