how realistic is this project for my bike

I am building a moped and I want to make an arduino powered computer for it. I want the computer to be able to calculate speed with a magnet switch and display the speed on a dot matrix screen, give it turn signals, brake lights, and a head light that can be activated by a light sensor, I would also want the screen to indicate when the turn signal is on and the head light is on, the final thing that I want is the engine temperature is. how possible would it be to make this? I am new to arduino and I do not know what the capability of arduinos are.

Hey, that sounds very possible and like a very nice project. I think you should read up on the individual sensors and try them in a "stand-alone" mode. Once you have an understanding of how they work you can easily combine them to get a bike computer as you want it.
There are lots of tutorials online covering blinking lights and temperature/light sensors. The LCD-screen would be the most difficult part for me (I haven't work with that yet), but I think there are libraries availbale that makes it easy to use.

Good luck with that project!

I already have a large knowledge of electrical engineering and how various sensors works

I would drive the direction signals and brake lights directly from the corresponding switches, and just provide 5V inputs to the Arduino to let it know when the signals are active so it can display that status. The automatic headlamp would be more complicated because you will need to use an LDR or similar to detect the light level, and then operate a relay to turn the lighting on. You will need a driver circuit between the Arduino and the relay.

I don't know where you would measure the engine temperature from. If the engine has already got provision for a temperature sensor then obviously you would use that. If not, you will need to add your own, and how you do that would depend what sort of engine it is. For a water cooled engine, I would look to install an OEM coolant temp sender into the water system. For air cooled, I guess you could mechanically attach a thermister to the engine casing, although I don't know how accurately that would reflect the engine's internal temperature. In my experience engine temperature sensors are usually thermisters, which are electrically very simple to use.

for the turn signals, I would have 5 LED's in a row. sequence them for the direction.

first thing that came to mind was a generator. used to have one on my bike when I was a kid.... alas, you probably have a power source.
http://www.woodengenerator.com/Related%20Sites.html

also, you may want to input wind speed.

tire revolution would offer ground speed, and you could total and log that for distance.