Internal water leak somewhere in toilet I think

I've been hearing a pump like sound, sounds like water is being pumped into the toilet on and off. The flow seems to be off. I will try to get a video if I can capture the right moment for the sound that I hear. I'm guessing I have to replace the toilet valve, but it could just be the flapper too. Thoughts? Thank you very much.

Put a few drops of food coloring into the back tank. If any of the color bleeds over into the bowl, that is proof that the flapper is leaking.

The fill tube is pushed too far down the overflow.
That will siphon water from the tank.

It also looks like the flapper valve may not be the right one for your toilet...and, it is starting to wear out. The flapper is collapsing (rubber is getting softer and taking a set)- the sealing edge should be horizontal, I think if you look at it, you'll find it is at an angle. Also, it is not centered and covering the full seat. It may work for awhile when new, but won't last as long as the right one for that toilet.

The flapper looks to small to me too.

Do you hear the fill valve running from time to time? If so, it's not the fault of the fill valve. It's probably fine. If there is actually something wrong with your toilet, most likely it is refilling the tank bit by bit for the water that is dribbling out of it. As Cacher Chick says, just drop in some food coloring in the tank and then check the bowl after an hour or so (or turn OFF the water for a few hours after marking the level of water in the tank with a pencil, and see if it is lower without being refilled).

If either test shows leakage from tank to bowl, it's probably the result of (1) As Terry points out, that refill tube is shoved into the overflow riser; it needs to be only the absolute end tip that goes in there, the rest of it can stay above it (or you can cut it a little shorter if you have to); or (2) that dead-looking flapper needing to be replaced, something you can do for a net outlay of about $4.50.

As everyone points out, that flapper looks a little dicey. Something like this Korky flapper (the brand most recommended on here and the original inventor of the flapper) should work fine: http://www.homedepot.com/p/Korky-Plus-2-in-Toilet-Tank-Flapper-2001CM/202310507

Come back and let us know what you find out.

All of you are right! It was the flapper. When I put the new one on, it still looks like it might be a tad off, but it stopped the leaking, that's for sure! Better than an extra $35 down the drain per month. I decided to go with a flapper that saves on water. So I see the flush is not as strong and I have to hold the toilet switch longer. At least I'm a patient person!

I have ended up saving about $2-6/ month with this economic water flapper. What is also nice is that it's in a bathroom that guests don't use often, so they are not so likely to push the flusher too hard for it So, you can tell at this point, I got my money's worth

That's great! Glad we could help. And thanks for the update. That flapper more than paid for itself.