Hi Milfoil
I think this is an anxiety type of dream. The rainbow serpent tried to bite you and I wonder if you felt fear or not? Dreams of being scared of being bitten by a snake are a classic anxiety dream but this dream is not exactly this picture, it's a little different. In the second dream you were worried for others with the cats. The first dream did have an aggressive animal that affected you but the second dream was more of a worry "what if" sort of dream.
The symbol of the rainbow is an interesting one and one I have had experience in my own life. I dreamt of a rainbow ankh about a year ago and it started a huge transformational spiritual phase in my life. Rainbows symbolise coming together, all the colours form with crystals and chakra work to create a balance. In the LGBT community each colour originally represented in the rainbow flag, represented something like life, spirit, healing, nature (which we always forget these days doh!) and so the rainbow was a coming together of diversity. So it could be a coming together of many elements in some sort of healing or spirit work. Other ideas about it could be success, good fortune and also the link between two worlds maybe? Earth and the higher self.
It seems quite important that the creature is not a snake, it's a serpent or eel like. I have been researching this and something more serpent like, rather than snake like, is more symbolic of good and evil (with all those old tales about serpents). Eels as a symbol are more slippery but you don't describe it like that at all. If you think it is a slippery type eel, it could represent feeling something is sliding out of your hands. I would interpret the first dream with the symbolism and my intuitive take as, something is near completion in your life. I see the serpent as that cycle and it is aggressive to you, like you are having problems finishing the last stage, this could also be anxiety about finishing something. I think the matter it relates to is to do with the rainbow colours, I feel maybe it's to do with your spiritual studies and you are frustrated about finishing something you are studying or can't quite master it! It's theme is definitely a block to completion! How can you get past it?
The second dream had four different cats which again show diversity together like the colours of the rainbow. I think that you don't normally have them together because they are from different places on Earth and probably wouldn't be friendly to each other. But I may be over analysing that
But they are different species together. They are not aggressive or a danger to you like the first dream. This dream might represent dealing with a burden in your life, this is almost like juggling and keeping all the balls in the air. 4 cats and keeping them in an enclosure and keeping people outside safe. Perhaps you are dealing with someone else's burden because you are worrying about other people here. Final idea on this dream, it could be a fear of letting something release about yourself, it could go wild and unpredictable, maybe lose you friends, so you have to keep it caged up at the moment and fear it being released from what you can control.
just some of my ideas, hope it helps Milfoil