Not only do you and your mother care for each other deeply, your minds appear to perfectly in synch. You each are dreaming of the other’s safety -- on the exact same night!
I agree that your upcoming move, in January, is most likely the cause of these dreams. Because water is a consistent symbol for emotions in dreams, your mother’s “fall” into a lake or canal most likely represents concerns you have about her ability to “stay afloat” -- emotionally -- without you. Although your mother does not know how to swim in real life, it is significant that, in the dream, she learns quickly -- with her daughter’s coaching. What is the message implied by this familiar dream metaphor? After an initial shock (your departure), your mother will indeed to “learn to swim” (live without you) in the emotional waters created by your departure.
Similarly, your mother’s concerns -- as she prepares for your absence -- are represented in her dream by an intruder. She worries that danger lurks near you, but she is warned by the intruder to “not even think about” expressing these fears to you. While it is possible your mother is concerned for her own safety once you are gone (she will be alone in the house more often), another interpretation of this dream is that she is aware she must not burden you (must not call out) with fears and anxieties concerning your departure. Your mother appears resolved to “let you go” so you can enter the next phase of your life.
Rather than foreshadowing actual future events, your dreams -- like most dreams -- appear to be providing us with a poignant glimpse of the present. By giving your mother support and reassurance, you are already teaching her how to swim. By “swallowing her fears,” your mother is allowing you to grow into the independent woman she truly wants you to become.