Η συνεργάτιδά μου με βοηθάει όταν έχω πολλή δουλειά.

In Greek, it is very normal to use the definite article with a possessive:

• η συνεργάτιδά μου = my colleague
• literally: the colleague of mine

So the article η is not optional here in normal Greek. It agrees with συνεργάτιδα, which is feminine singular nominative.

Συνεργάτιδα is the feminine form of συνεργάτης.

It can mean:

• colleague
• coworker
• associate
• female collaborator

The best translation depends on context. In this sentence, colleague or coworker is usually the most natural choice.

This is because μου is an enclitic word, meaning it is unstressed and leans on the previous word.

When a word like συνεργάτιδα is stressed on the third syllable from the end, adding an enclitic like μου often causes an extra written accent:

• συνεργάτιδα
• συνεργάτιδά μου

This is a spelling and stress rule in Greek. You will see the same thing in other phrases too.

The short possessive forms in Greek usually come after the noun:

• η συνεργάτιδά μου = my colleague
• το βιβλίο μου = my book
• ο αδερφός μου = my brother

Putting μου before the noun is not the normal pattern.

If you want extra emphasis, Greek often uses:

• η δική μου συνεργάτιδα = my own colleague / my colleague

But the basic everyday form is η συνεργάτιδά μου.

Με means me.

It is the direct object pronoun of the verb βοηθάω / βοηθώ:

• με βοηθάει = she helps me

So the structure is:

• Η συνεργάτιδά μου = subject
• με = object
• βοηθάει = verb

English also uses a direct object here: She helps me.

Because the subject is η συνεργάτιδά μου = my colleague, which is third person singular.

So the verb must also be third person singular:

• εγώ βοηθάω = I help
• αυτή βοηθάει = she helps

In this sentence:

• Η συνεργάτιδά μου με βοηθάει = My colleague helps me

Yes. In everyday Modern Greek, both βοηθάει and βοηθά can be used for he/she/it helps.

So these are both possible:

• Η συνεργάτιδά μου με βοηθάει
• Η συνεργάτιδά μου με βοηθά

Both are natural. βοηθάει may feel a little fuller or a bit more colloquial in some contexts, but both are standard and common.

Because Greek uses the present tense here for a habitual or repeated situation:

• όταν έχω πολλή δουλειά = when / whenever I have a lot of work

The idea is not one single event, but something that happens from time to time.

Also, after time words like όταν, Greek often uses the present where English might also use the present:

• όταν έρθει / όταν έρχομαι / όταν έχω etc., depending on the structure and meaning

In this sentence, the present tense is completely natural.

Literally, όταν means when, but in a sentence like this it often has the sense of whenever.

So:

• Η συνεργάτιδά μου με βοηθάει όταν έχω πολλή δουλειά

can be understood as:

• My colleague helps me when I have a lot of work
• My colleague helps me whenever I have a lot of work

The habitual present makes the whenever sense very natural.

Because δουλειά is a feminine singular noun, and the word meaning much / a lot of must agree with it.

So you get:

• πολλή δουλειά = a lot of work

Compare:

• πολλός = masculine
• πολλή = feminine
• πολύ = neuter or adverb

Since δουλειά is feminine, πολλή is the correct form.

Because δουλειά here means work in a general, uncountable sense.

So:

• πολλή δουλειά = a lot of work

If you used the plural δουλειές, it would sound more like:

• many tasks
• many jobs
• many chores

So there is a nuance:

• πολλή δουλειά = a lot of work in general
• πολλές δουλειές = many individual tasks/jobs

Greek word order is fairly flexible. The sentence you have is a neutral, natural order:

• Η συνεργάτιδά μου με βοηθάει όταν έχω πολλή δουλειά.

But other orders are possible, especially for emphasis:

• Με βοηθάει η συνεργάτιδά μου όταν έχω πολλή δουλειά.
• Όταν έχω πολλή δουλειά, η συνεργάτιδά μου με βοηθάει.

The meaning stays basically the same, but the focus can shift slightly. The version you were given is a very standard, good default word order.