Learn Finnish: Minä olen työssä aamulla. - I am at work in the morning.

Both mean "at work." The base word is työ (work). työssä is the singular form (literally "in the work"), while töissä is the plural form. You will hear the plural töissä much more often in everyday spoken Finnish, but työssä is grammatically correct and good to recognize!

Why does the word for morning (aamu) have the -lla ending here?

The -lla or -llä ending is often used to mean "on" or "at" a physical place, but it is also the standard way to express parts of the day. Adding -lla to aamu is how you translate "in the morning."

If I make this sentence negative, do työssä or aamulla change to the partitive case?

No, they stay exactly the same: En ole työssä aamulla (I am not at work in the morning). The lesson rule about using the partitive case in negative sentences only applies to the object of the sentence (the thing being acted upon). Words that tell us "where" (työssä) or "when" (aamulla) use their specific location and time endings, not the partitive.

Can I drop the word Minä and just start the sentence with Olen?

Yes! Because the verb olen (I am) ends in -n, it already tells the listener exactly who is doing the action. In everyday Finnish, it is very common to leave out the pronouns minä (I) and sinä (you).