Can I add the date and initials automatically?

Short answer: Yes — your name and today’s date fill themselves in, and saved initials are one tap. The common fields are the fastest part.

Yes — and this is quietly the biggest time-saver in the app. On most documents the signature is only a third of the work; the rest is dates, initials on every page, and printing your name legibly. Signed treats those as first-class fields:

Date — drops in with today's date already filled. Tap, place, done.
Initials — create them once (draw, type or generate, same as your signature), save them to your library, and stamp them on every "initial here" line in seconds.
Name and text — your printed name fills itself in; free text fields cover the "occupation" and "unit number" blanks.
Checkmarks — for the tick-box clauses, without trying to draw a convincing tick with your finger.

The result: a five-page lease with initials on every page and three date fields takes about a minute, not a wrestling match.