Speed and rpm is jumping around at same time why

Go to Autozone, or any chain auto parts store. Have them read your engine trouble codes. It's called an OBD reader.
The trouble code is a 4 digit number that should tell you what component on your engine is faulty.

Could possibly be your Vehicule speed sensor that doesn't work correctly . Best way to know is to check for engine codes . But you'll need to have an obd2 scanner.

Have it scanned for free at Big autoparts stores and that should point you in right direction of faulty component. If not, get back to us with scan results.

After I had the throttle body of my 2005 mazda3 cleaned, the RPMs would jump drastically - bouncing back and forth up to 16 times! The service manager seemed perplexed...and ultimately the solution was TIME. The bouncing gradually diminished and then stopped...can't remember for sure, but it was probably over about 6 weeks, maybe about 1000 miles.

1st run scans for fault codes.

Did you check the voltage after a drive or after it was jumped. The battery may need some time to recharge if it was jumped before it gets checked. Have you checked for a possible draw on the battery? This could be a reason it dies every once in a while. I think that the Alternater is on its way out, it doesn't sound like it is charging like it should. It the new belt tight enough(some new belts stretch after a short time)

It could be your transmission trying to find the right gear it will jump around on diffrent road surfaces and going up hills/down hills. It is usaully noticable on cruise because it is at a constant speed and your thinking why would it need to shift. Sometimes it doesnt even really shift the gear its so inbetween it just jumps back really fast.

check the idle speed .. it probably should be around 600 rpm .. if its higher then the transmission will jump ... that is probably controlled by an idle speed sensor ..

Your instrument is bad, The spiral coil for the needle is alraedy out ot calibration therefore it has been jumping around. Even they reset, it already been stretching. It needs a new one.
Don't waste mony for the reset.
It is probebly expensive from dealer plus labor. Just to check out the price,
You can get a used one from ebay for $85. However, you need to know how to replace it. Let me know it you need any help.
Meanwhile you can gauge your RPM to keep your speed under control on the long trip.For example: 2000 rpm is about 55 mph. Try to keep it below 3000 rpm so you don't get over speed limit.

you need to check your ignition system it seems like you have a coil or module or crank sensor breaking down you should see if you have any stored codes good luck