Ticking noise when I release acceleration

The best suspect is an exhaust leak, but those typically cause the ticking noise during acceleration. I'd start by having the exhaust system inspected.

Sounds like the hamsters are trying to get off the wheel! The first thing that came to mind is an emissions-related solenoid pulsing on and off. Some are designed to only operate when higher road noise makes them impossible to hear. Some operate all the time and make a thumping noise, but most of those are mounted on a rubber bracket or isolator. I've run into a few where the rubber deteriorates, then the solenoid's pulsing transmits into the car body where it is amplified and becomes easier to hear.

Two things to consider include a collapsed engine mount, and a worn outer CV joint. The mileage you listed is too low for these to be good suspects, but given the nature of the symptoms, a collapsed mount can let the engine rock too much between the forces from accelerating and coasting. If the two metal parts of the mount are able to touch each other, engine vibration will be transmitted into the body where it can often be felt. Worn outer CV joints make a clicking noise, but that usually occurs when turning and backing up. That noise would not be limited to third gear. In fact, it is rarely heard at any speed other than a very low speed.

There is a tool you might be able to borrow or rent from an auto parts store that borrows them called the "Chassis Ear". It is a set of six microphones, a switch box, and headphones. You clip the microphones to suspect points, then drive around while listening with the headphones. You can move the microphones around to zero in on the source of the noise. Be aware that many mechanics have never seen or even heard of this tool. Suspension and alignment mechanics use it to find rattles, squeaks, and other noises.

A broken engine mount is not a safety issue. One mount holds the engine from rocking excessively between acceleration and coasting. It has a rubber isolator to cushion the movement. When that isolator deteriorates, the two metal parts of the assembly can bang into each other. The bigger concern is the exhaust pipe connection, wiring harnesses, and fuel lines are being flexed more than normal, and that can lead to a failure.

If you hear a noise while turning the steering wheel, especially if you hear it more when the car is standing still, the upper strut mounts are good suspects. Reach over the top of a front tire, and wrap your fingertips lightly around part of the coil spring. Have a helper slowly turn the steering wheel. You should feel the spring rotate smoothly along with the wheel. If the bearing in the upper mount is binding, you'll feel the spring wind up and build tension, then suddenly pop free and rotate. That popping free, or any roughness, is what is heard inside the car. Those mounts will bind less and rotate easier when the car is moving.