Serious spoilers below.
The Owls. One of the first things you learn about Twin Peaks is that the owls are not what they seem. What that really means is never quite explained, like so much else in the show. Many have concluded that the owls are the eyes and messengers of BOB and therefore wholly sinister. I disagree. The owls are not just the tools of BOB, they are how all the spirits in Twin Peaks see and interact with the material world. Both those from the White Lodge as well as the Black Lodge. The only denizen we meet from the benevolent White Lodge is The Giant. Similar to his humanoid form, when he interacts through the owls he is seen as an enormous owl. Major Briggs more or less directly states that he saw the giant owl before visiting the White Lodge, and in her Secret Diary Laura describes having one vision of an enormous owl. This explains the import Log Lady sees in her message to Laura that 'Some owls are big.' It is her cryptic and unhelpful way of trying to tell Laura that there are not just forces of evil in Twin Peaks, but good as well.
The Tremonds. Pierre Tremond and his grandmother are two of the most mysterious figures in Twin Peaks. They appear only once in the series, when Donna delivers a meal to the seemingly bedridden Mrs. Tremond. They are given a much larger role in the movie, most notably giving Laura the painting that allows her to visit the Red Room in her dream and receive Coops warning about the ring.
There has been much debate about the nature of the Tremonds, including one interesting theory that Pierre is a representation of a young Leland. I do not agree with this theory. I believe Pierre is a lesser spirit of the Black Lodge. Who is the grandmother? It is Pierre's host, similar to how Gerard is the host to MIKE. However, unlike Gerard and Leland, Mrs. Tremond has been a host so long she no longer has any resistance left in her. This relationship is most clearly shown in the scene with Donna, where Mrs. Tremond seems visibly afraid of both Pierre and the creamed corn on her plate. Pierre then vanishes the creamed corn into his hands. In the movie creamed corn was made the symbol of 'garmonbozia,' the pain and suffering of humans which the creatures of the Black Lodge feed upon. In the movie, during the 'meeting' that Philip Jeffries describes, we see MIKE and BOB talking at a table holding a large bowl of creamed corn. In the background sit Mrs. Tremond and Pierre, along with several other characters who are never seen before or since. At Pierre's feet, and no one else's, sits a smaller bucket of creamed corn. All this seems to imply that Pierre is a spirit of the Black Lodge and that Mrs. Tremond is not.
The question remains as to what role Pierre's is playing in the events of the show and film. His nature and his presence at the meeting imply that he is, or was, a familiar of MIKE just as BOB once was, though of a lesser variety. As such, in his actions he seems to be helping in MIKE's crusadge against BOB. This is why he guides Donna to Harold Smith and why he gives Laura the painting. It is however an open question whether he is still under the control of MIKE or if he seeks BOBs destruction for his own reasons.
The Ring. Specifically, the green ring bearing the symbol of Owl Cave first shown being worn by Teresa Banks in Fire Walk With Me. It is found by Agent Chester Desmond under a trailer we later learn was occupied by The Tremonds. After finding it he disappears, and his disappearance coincides with the brief reappearance of Philip Jeffries at FBI headquarters. Jeffries describes a meeting between spirits of the Black Lodge where we see the dwarf, also known as The Man From Another Place and in this movie revealed to be MIKE or at least a part of MIKE, say the line "With this ring I thee wed." Later, in her dream, Laura Palmer sees the ring being presented to her by MIKE and Cooper warning her not to take it. At the end, Gerard is able to pass to Laura the ring while BOB is attempting to posses her. She takes it, and this seems to stop BOB's possession and so he kills her. What are we to make of this? Why does Cooper warn her away from the ring when it seems to save her from BOB?
Simply, wearing the ring makes a person the property of MIKE. This is how Chester is able to be taken by the Black Lodge and why Cooper warned Laura away from it. Even though it saved her from BOB, she is now under control of MIKE and this is why she is stuck in the Black Lodge along with Cooper. This is why BOB is forced to give up the garmonbozia generated by her murder to MIKE. This also means the garmonbozia generated by Teresa's murder belong to MIKE, and the scene where Gerard confronts Leland on the street may be because BOB did not give that garmonbozia to MIKE.
This brings us to the motivation of MIKE with regards to the ring. There are two possibilities. Either what he said to Cooper is true and he no longer wishes to do evil and hopes to stop BOB, in which case the ring and all his actions in the series are attempts to starve BOB of garmonbozia, or he was lying to Cooper, he is still an evil spirit and is simply competing with BOB for garmonbozia.
A side note, in the meeting with BOB, immediately preceding his "With this ring I thee wed" line, MIKE has the even more mystifying line where he comments on the green, formica table in front of him. I believe this is simply a strange way of bringing the viewers mind back to the green ring, cementing even more clearly the connection between it and the following line.