Learn Finnish: Äidin poimimat marjat ovat herkullisia. - The berries picked by mother are delicious.

The agent participle ending -ma or -mä describes an action 'done by' someone. The person who did the action is always put in the genitive case, which is why we use äidin (mother's). Together, Äidin poimima acts exactly like an adjective meaning 'picked by mother'.

Why is there a -t at the end of poimimat?

Because it acts as an adjective describing marjat (plural for 'berries'). Participles must agree with the noun they describe in both number and case. Since marjat is in the nominative plural (ending in -t), the participle poimima must also take the plural ending to become poimimat.

Could I use the past passive participle (poimitut) here instead?

No, because you are naming the specific person who picked them (äidin). The past passive participle (poimitut marjat, 'the picked berries') is only used when the doer of the action is unknown or unimportant. If you state exactly who did the action, Finnish requires the agent participle.

Why is herkullisia in the partitive plural instead of the nominative plural (herkulliset)?

When a plural subject is described by an adjective with the verb olla (to be), the adjective is almost always in the partitive plural. If you used the nominative plural (herkulliset), it would sound like you are equating them: 'The berries are THE delicious ones' rather than just describing them generally as 'delicious'.