Can I fit a wired cycle computer when I have front suspension?

You can definitely use a wired computer on a mountain bike with shocks. Simply make sure that wire has enough slack when the fork is fully extended and you will be ok. However, I would really recommend a wireless model. They are simpler to install and do not have the clutter of a wire running down your bike. In the woods, wires often get snagged by branches, trees, etc. With a wireless model that doesn't happen. Even with a lot of u se, the batteries last for over a season. A replacement battery costs about $4. I really feel that the benefits of wireless definitely outweigh the disadvantages.

Yes... Just use more plastic zip ties than supplied with the unit. And leave a little slack so that when that suspension moves up & down - the wire has room to move with it. Run the wire down the outer part of the fork, then bring it towards the sensor using more zip ties.

Yes you will have no problem the forks are extended as much as they will get when you put it on and the shocks are not going to move that far. I like to use clear packaging tape to hide the wire on the inside of the fork. Use the smallest zip tie you can find to connect the wire to one of the cables.

Yes you can. Run the wire along the brake wire to where it attaches to the fork, and from there you can zip tie the wire to the fork itself

...or run the computer's wire to the rear wheel, that one runs just as fast as the front wheel. Not all computers will allow this, but there are some computers (or accessory sets with longer cables) that permit fixing the sensor at the rear wheel.

Alternatively, drop that junk and use a GPS based computer ;-)

Yes, but you will still need batteries