Remote control missing: could have been taken as a prank, or just lost somewhere. Sometimes, it's hard to find what you're looking for, but when you're not looking for it, you find it.
A penny under the toilet. Someone could be dropping pennies from their pants pocket while using the bathroom.
Someone breathing... like how? Hyperventilating?
Guitar strumming on its own. Create a temporary rule in which the guitar is put away after being used. If you have a case for it, put it in there.
Essentially, eliminate all the possible things that could be causing these strange phenomenon. Run some possible tests as to what is actually happening. Once you're done w/ that throroughly and can't explain some of the things, then who knows. May it is haunted. Maybe it's all coincidental.