Fugi Z10 I managed to insert the battery in the wrong direction and is stuck now. Is there a straight forward way to remove or is a job for a specialist? After removing battery, which was inserted wrong way, camera is not working, even though battery is charged.. Would the camera be damaged or should I just buy a new battery?

Put a pressure by youre hand beacause its old and stuck

Turn the petcock to the OFF position! Remove and clamp off all fuel, air, vacuum lines. Then, remove all mounting bolts/nuts. You may have to remove the seat or anything else that prevents its removal. It might slide directly backwards due to rubber mounting grommets. Look carefully...should be a straight forward job.

The battery is located under the rear seat on the passenger side. The replacement battery is a little more costly given the fact that it has the need for venting sulfuric acid fumes. If you remove the old battery and do not place a temporary power supply on the systems computer, you will possibly cause may things to go wrong. The temporary power supply insert is on the drivers side directly under the steering wheel. You will need the adapter plug. Your best bet is to go to advance, autozone, walmart, etc., and plead with the manager to allow free installation of battery you intend to purchase. Show them how clean the underside of you back seat is and there is no battery leakage. Liability keeps many shops from installing back seat battery compartments due to acid, leather, etc. I talked a kid into it at advance for 5 bucks. Otherwise, professional dealer or shop installation will cost you more on top of the already overpriced $170.00 battery. Back seat removal is easy. Pull front of back seat straight up on both sides releasing tabs, then lift it and slide rear of seat up and out. Installation is the same in reverse.

Press your trash can button which is also green to the right of your menu button. This will solve your problem

The most likely problem you have is a partially stuck open cooling system thermostat. The coolant is constantly flowing through the radiator, so its not warming up as required. This in turn will increase your fuel consumption considerably. The alternator needs to be removed to gain access to the front of the engine block where the thermostat is located. Its a fiddly job, but straight forward for a competent mechanic. Another common fault also related with the cooling system is a faulty coolant temperature sender. Again a straight forward part to replace if needed.
Hope this helps you.

Battery is behind the front left wheel. You have to remove the wheel to replace the battery. (you can access the battery w/out removing the wheel, but you can't actually get the battery out unless you take the wheel off.)

Once the wheel is off, remove the inner-fender well mud-guard and you will see the battery just forward of the wheel well. From there it's pretty straight forward.

Once this is removed, you should be able to see the battery hold-down bolts.

Remove these and remove the hold-down assembly.
If you are removing the battery, remove the 1st battery cable.

Depending upon what battery you have, you may be able to slide the battery back toward the wheel and disconnect the 2nd cable.

Jack the vehicle up, put on jack stands and remove the passenger side wheel.

On the front side of the wheel well there is an access panel that needs to be removed in order to access the battery. There are 6-8 1/4" screws to remove. Then manipulate the cover until you can remove it, bending it slightly.
If you were unable to disconnect the 2nd battery cable earlier, you can now move the battery further towards the rear of the car. Remove the 2nd cable clamp from under the hood.

Slide the battery all the way out. It is heavy!
Reverse the instructions for reassembly.

Turn the camera on and press the menu button. Press the down arrow to get to the line that says "set". Press right arrow. Press down arrow until you highlight icon of person talking. Press right arrow and pick the correct language.

This is pretty common. Get some small pliers, which are known as "duckbill" needle-nose pliers. They're flat, needle-nose pliers which will allow you to stick the tips into the small space on top and bottom of the stuck battery, and gently wiggle it out. If it's really, really wedged in, you may pull off the end cap of the battery, if you're not careful. At that point you'd still need to remove the battery's remains, and get yourself a new one (battery, not camera). I've saved several customer's cameras this way. Good luck.

Your camera is broken. This should not happen. If it's in warranty, send it to Fuji for a replacement.