Help sort out Cable Distribution

We closed on our house last Wednesday, March 14th. We've got a month to officially move in and before that I'd like to do structured wiring from a central room upstairs. There is currently no ethernet run through the house, so that will be all brand new. My question is regarding the existing coaxial cabling.

Cable signal comes into the garage from the tap and plugs directly into a power outlet. (See attached picture) All the previous owners could say about it was that it was installed by Comcast and that it was likely an amplifier. So how does it work? Each of the bedrooms and the living room have coax run to them, but I can't for the life of me figure out how each room is receiving the input signal.

1. Are there splitters hidden in the walls somewhere?
2. Can I leave all the existing cabling in the walls and run my own and connect it to the cable incoming from the garage?

I've done a lot of research about structured wiring, but I have very little understanding of how our house is currently setup. I want to reuse as much as possible.

Thanks for any help in advance.

Thanks for all the advice. We're stopping by the house to pull the trash out to the street. I'll take a look behind one of the wall plates and see what I can find. I'll bring a ladder tomorrow and head up into the attic to what I can find there.

My initial design was to pull CAT5e and Coaxial into each room. Is the cost negligible between CAT5e and CAT6 now? My plan was also to run at least two RG6 drops to each room.

I guess the next step is to scour the attic and trace the cables as much as I can.

I'll let you all know what I find.