Learn Dutch: Zij heffen het glas naar de hemel. - They raise the glass to the sky.

This sentence actually uses the regular present indicative plural (heffen). It is likely included to set the scene for a toast, which is exactly the context where you'd hear fixed subjunctive expressions like Leve de... (Long live the...) or God hebbe zijn ziel (May God have his soul).

Why use heffen to mean "raise" instead of a more common verb like optillen?

Heffen is slightly formal and is the specific verb used in the fixed expression het glas heffen (to raise a glass / to make a toast). Optillen is used for physically picking up an everyday object, like lifting a heavy box off the floor.

If "they" are raising glasses, why is het glas in the singular?

Dutch frequently uses a distributive singular when multiple people each interact with one of the same item. Because each person in the group is raising one glass, using the singular het glas sounds perfectly natural, much like saying "they raised their glass" in English.

Does de hemel mean "the sky" or "heaven" here?

It means both! De hemel is the Dutch word for both the physical sky and the spiritual heaven. In the context of a toast, raising a glass naar de hemel could simply mean lifting it high into the air, or it could symbolize a toast to someone who has passed away.