Learn Hardcore German: Bitte berücksichtigen Sie die Frist. - Please take the deadline into account.

Sie is the formal you in German and is always capitalized in standard writing to distinguish it from sie (she/they). It can refer to one person or more than one; the form is the same. Only context tells you whether it's one or many.

How is the imperative formed with Sie in Bitte berücksichtigen Sie ...?

For the polite imperative, German uses the verb in its infinitive form + Sie: Berücksichtigen Sie ...; Gehen Sie ...; Nehmen Sie ....
Bitte is a politeness marker and can be added; it does not change the imperative formation.
A more indirect, very polite alternative is: Würden Sie bitte die Frist berücksichtigen?

What case is die Frist, and why is it die?

Frist is a feminine noun (gender: feminine).
It is the direct object of berücksichtigen, so it stands in the accusative case.
Feminine nouns have die for both nominative and accusative singular, hence die Frist is correct (not der/dem Frist).

Is berücksichtigen the same as beachten or einhalten?