Small pieces of matter in a fluid - flecks of dust, pieces of pollen, smoke particles, etc. - seem to vibrate randomly because they are being constantly hit from all sides by the molecules of the fluid (water, air, etc.)
The property of most matter that matter expands as heated and contracts as cooled. All matter is in a constant state of motion, the faster they move, the more space they need to move in and push the other molecules away. Thus as solids and liquids (phases of matter with definite volumes) increase temperature, the molecules move more and take up more space, so the substance increases in size.
The quality of matter that substances in materials where atoms are free to flow (gases or liquids), small particles put into the fluid tend to spread out randomly until they are evenly mixed (go from areas of high concentration to low concentration). This happens because both the fluid and the particles are constantly moving, so will be pushed and dragged around by other molecules until they mix evenly.
When the molecules of the fluid change temperature, say upwards, they move more, this causes them to take up more space (thermal expansion). The fluid in the thermometer has nowhere else to go, so it rises up the tube. The reverse is true for falling temperatures.
The temperature doesn't change, because all the energy gained or lost by the substance just goes to changing the state of matter, not the temperature (the energy gained breaks bonds of attraction between neighbouring molecules instead of changing their speed, or the energy lost goes to forming bonds of attraction between neighbouring molecules instead of changing their speed)