I was thinking this could be my first arduino project as it seamed simple in theory, but is seams I was wrong
It's a very doable project, if you get rid of the requirement to power it from a coin cell for a year. You will either need much more power than that, or you will need to spend most of your effort making the project consume as little power as possible.
But just for example if I wanted to build it just to learn would these parts be suitable?:
Reasonable parts. You may wants consider a reed switch which uses a magnet to activate it, rather than a micro switch with a lever. It will be easier to install, and is what most alarm systems use. Reed switches with a matching magnet for doors and windows are readily available.
Or if I where to buy a cheap door sensor how can I make any of the examples flash a led on another arduino when door opens wirelessly?
I assume you mean an existing wireless door sensor? The trick there is going to be receiving the signal. If it includes a receiver I both a set of relay contacts, it's a trivial project. If there is no receiver included, it gets more complicated, and using a pair of Arduinos and RF transceivers may be easier and more fun.
If you want to run the receiver off of a battery, you're going to need something to switch the radio power off. And you will still want to use low power standby modes as much as possible in the processor. If you can use an AC wall wart power supply, the power management concerns are not important.
For the receiver side, you will want to power that off of a wall wart or a very substantial battery. That's because you won't be able to turn off the receiver radio to save power - it needs to be on and receiving all of the time in order to pick up the transmitter's signal.
This sounds like an interesting project: simple enough to not be overwhelming, but enough technical challenges to make it interesting. Just start out with a solid unlimited power supply (wall wart or USB) to get it working, and then move to batteries as you refine the power budget. As you improve the power utilization, you may get to the point where you can use smaller batteries, but don't expect to get to a coin cell without spending quite some effort.