So I moved into an apartment with my boyfriend about a few months ago; however, some really strange things have been happening lately.
In my kitchen we have this old coffee mug full of spare change: nickels, pennies, etc. Around maybe 8:00 pm I heard this noise come from the kitchen, almost sounded as if the coffee mug fell off the counter and hit the floor. I went to go investigate and instead I find the coffee mug not tipped over, but sitting perfectly still on the ground with all the change still inside it sitting perfectly straight up as if someone had moved it from the counter to the floor. Now my boyfriend was working late shifts and I have not a single pet. So I thought that to be pretty strange.
A few nights after that my boyfriend and I were in bed sleeping, I woke up around 1 am for no reason. We have a window across from our bed, and I saw this dark shadowy blob-like figure right outside the window. Just when I thought things couldn't get worse, it moved from the window up to our ceiling and I suddenly felt like I couldn't move, speak out loud, I could even hardly breathe. I kept cursing at in my head to go away but it kept getting closer.
Now, I was not a very religious person before this happened, but I prayed and I prayed hard to God and not even moments after I was done with my prayer, the black shadow immediately banished and I felt like I could move, breathe, and speak. I do not claim any religion today, but I can say that I do have a belief that there is a God after that experience.
Just thought I would share my experience, since no one would believe me if I told them this story.
As far as the second incident is concerned, I feel that it could be sleep paralysis from the way you described it.
But as Argette said, the first incident seems more like a paranormal than the second one. But keep us posted of any further experiences so that we could give some suggestions.
Regards and respects to you.
SDS