It should be do-able
Search the forum there are lots of people that use the Arduino in their cars, and bikes including some race cars etc.
In terms of your requirements....
Firstly the input from the sensors.
You will need to measure the voltages that come from all of these sensors (and go into your existing display).
They may be voltages e.g. for oil pressure 8 V could = 50psi etc, but you'd need to determine what voltage matched with what values
Its also possible that these are not just voltages, the values could be conveyed by different currents from these devices, but it seems less likely.
As you are not reading RPM's etc you will probably not be reading pulses, but its hard to know what data comes from the sensors until you take a detailed look.
As you have a lot of inputs, the smaller Arduino's e.g. Uno, won't have enough analog inputs, you'd need to use a Mega2560 which is bigger and has more analog inputs
Re: Display etc
I'm playing with using a cheap Android tablet as a display myself at the moment (though I've not had time to do much)
The easiest connection is via bluetooth, but if the tablet you intend to use doesnt have bluetooth, its possible directly connect via USB if the tablet support OTG aka USB Host. Most tablets seem to have this even if its not in their spec.
I found my $50 7inch tablet had this feature, I just needed to buy $2 cable to plug into its normal USB port.
I was then able to connect to the Arduino.
However unless you are a Android developer, I suspect getting something that looks good on the tablet may be a steep learning curve.
To be honest, if you've not used the Arduino before or don't regularly mess around with electronics it will also be a steep learning curve