This is "I of Newton", an episode of the 80's revival of The Twilight Zone. It basically goes as you remember:
Sam asks if there are any physical limitations to the demon's powers, and for his third question, if there is any place from which the demon cannot find his way back. The demon denies any limitation in either regard. Sam then delivers ...
I believe this is Mirror, Mirror (1995–1998).
The Wikipedia page offers a pretty detailed rundown of the plot, which appears to match your description:
When fourteen-year-old Jo Tiegan is shopping with her father in 1995, she notices an antique shop which she feels a compulsion to go to. There she sees a beautiful oval mirror, which she is given as a gift ...
Could it be Mighty Max (1993)?
The series follows Max, an adventurous teenage boy who receives in the mail a small statue of a fowl, inscribed with Egyptian hieroglyphs whereof the translation states: "You have been chosen to be the cap-bearer. Go to the mini-mart and wait for a sign, Mighty Max". Shocked by the message, Max drops the statue, ...
There's not much information online about it, but is it possible this is Captain Zep - Space Detective?
Wikipedia says this about the show:
Captain Zep – Space Detective is a British television children's series produced by the BBC between 1983 and 1984.
Constructed as part drama and part quiz game, Captain Zep featured mysteries that would be solved by ...
Although you say "Not Who" it is somewhat similar to the story Doctor Who and the Silurians.
Date - 1970, several years earlier than Beasts.
The premise is that a race of intelligent creatures from Earth's past have been in suspended animation for millions of years. They are beginning to wake up, and want to take back their planet.
Sounds like Kaijudo: Rise of the Duel Masters (2012-2013).
Kaijudo is a 2012 American animated series and trading card game that serve as a spin-off and relaunch of the Japanese Duel Masters franchise. The animated series was produced by Hasbro Studios, animated by Moi Animation in South Korea, and developed by Henry Gilroy and Andrew R. Robinson for ...
Could this be Puttnam's Prairie Emporium?
It didn't take place in a diner, but rather and old-fashioned five and dime store.
Many of the other details fit.
It was a Canadian television series that ran for 52 episodes during 1988-1990. It was syndicated in the US, possibly on PBS.
There were two children that lived with their mother and the eccentric owner of ...
Mighty Max (1993–1995)
Max (Rob Paulsen), a twelve-year-old boy, finds a magical cap that can teleport him across dimensions.
Mighty Max on IMDB
The artwork depicts him as wearing a red baseball cap with a big yellow M at a very 90's angle.
Found by searching for: "red hat cartoon alternate dimensions OR worlds"
Might this be Zinba...?
The juvenile Kan from the earth is summoned to the Kingdom of Toria , where he encounters attack from the giant creature Zinba, and he's rescued by the linker Shibuki and Uranus. Later, he accidentally gets on the linker squad DUX truck to the maze valley, finding in a cave a golden Zinba.
The main character is, Tian Yu, a boy from ...
The answer by @M.A.Golding notes some uncertainty about whether various early shows had episode titles originally or if the titles were assigned retrospectively, so I thought I'd look for the earliest example of onscreen titles. M. A. Golding's answer references Tales of Tomorrow, many of the episodes have been posted on youtube playlists here, here and here,...