Instructions for handling toxic liquids
Each liquid produces some vapours. When you leave wet clothes, they eventually dry. Same here. It is true, that vapour pressure for mercury at room temperature is extremely low, but since mercury accumulates and has quite high toxicity, it is still a trouble. Same for other liquids.

Mercury must be kept in sealed container and/or under layer of water. Any works with it must occur in large pan, so no tiniest drop of mercury escaped. Escaped drops must be collected using thin copper plate, washed in concentrated nitric acid. All solutions of mercury compounds and remaining mercury should be utilized according to local procedures (there is an agency for it at my city). Metallic mercury may be transformed into salts using $\ce{FeCl3}$ concentrated solution. While not removing the mercury, this transforms it into compounds that does not produce vapours. However, in case of mercury leak a special agency must be informed to perform all necessary procedures. Consult local regulations on the cases.

Dichloromethane has regrettably low boiling point. It must be kept away from heat sources and in case of high temperatures it must be cooled or kept in sealed container. It evaporates swiftly on open air, carrying away much heat.

All the liquids should be used under fume hood. In case one is unavailable, an acceptable alternative is open air as long as there is a gentle wind. The chlorinated hidrocarbons mentioned has strong odor, strong enough to make handling them without good ventilation impossible. None of the liquids should contact skin. It is not immediately fatal, but still. In case the contact occurred, the chloroalkanes will evaporate quite quickly, though washing skin with soap and water is highly encouraged. Again, one-time breathing-in of the vapours is not fatal with this compounds, but repeated breathing-in guarantees health problems.

Good thing: none of the liquids is flammable, so flammability is not a trouble here. Unfortunately, heating them at presence of air is still highly unrecommended as well as continuous exposure to sunlight: it may produce phosgene.