Minä pyydän sinua auttamaan minua.

Yes, it can be omitted.

In Finnish, the verb ending already shows the subject, and pyydän means I ask / I am asking. So the sentence can simply be:

Pyydän sinua auttamaan minua.

Adding minä makes the subject more explicit. It can sound emphatic, contrastive, or just slightly more deliberate:

Minä pyydän sinua = I’m asking you / I am the one asking you

So both are correct, but without minä is often the more neutral version.

It is the present tense.

Finnish does not have a separate verb form for the English progressive am asking. So pyydän can mean:

• I ask
• I am asking

The exact meaning depends on context.

Because Finnish verbs often change their stem when they are conjugated.

The basic form is pyytää = to ask.
In the minä form, it becomes pyydän.

This is a normal stem alternation in Finnish. You can think of it as something you learn together with the verb:

• minä pyydän
• sinä pyydät
• hän pyytää

So pyydän is just the correct 1st person singular form of pyytää.

Because sinua is the form required by the verb pattern here.

The verb pyytää commonly uses this structure:

pyytää jotakuta tekemään jotakin
= to ask someone to do something

In that pattern, the person being asked is in the partitive case:

• sinä = you
• sinua = you (partitive)

So:

pyydän sinua = I ask you

It is best to learn this as a pattern: pyytää + sinua/häntä/minua + tekemään...

Auttamaan is a special infinitive form of auttaa = to help.

The grammar name is the third infinitive illative, often called the -maan / -mään form.

Here:

• auttaa = to help
• auttamaan = to help, in the pattern used after verbs like pyytää

So in this sentence:

pyydän sinua auttamaan minua
= I ask you to help me

This is a very common Finnish structure: pyytää jotakuta tekemään jotakin

Examples:

• Pyydän sinua tulemaan. = I ask you to come.
• Pyydän häntä odottamaan. = I ask him/her to wait.

Because after pyytää, Finnish normally does not use the basic infinitive auttaa.

Instead, it uses the -maan / -mään form:

• correct: pyydän sinua auttamaan minua
• not normal: pyydän sinua auttaa minua

So this is not a word-for-word match with English to help. Finnish has its own structure, and after pyytää, that structure is tekemään, not the basic infinitive.

Because auttaa normally takes the person being helped in the partitive:

• auttaa minua = help me
• auttaa sinua = help you
• auttaa häntä = help him/her

So minua here is not there because of pyytää. It is there because of auttaa.

That means the sentence has two different partitive objects for two different reasons:

• sinua after pyydän
• minua after auttamaan

The most neutral word order is:

(Minä) pyydän sinua auttamaan minua.

Finnish word order is fairly flexible, but changing it usually changes the emphasis.

For example:

Sinua minä pyydän auttamaan minua.

This sounds more marked, as if stressing you in particular.

For a learner, the safest choice is to keep the neutral order: Pyydän sinua auttamaan minua.

Yes. It is grammatical and natural standard Finnish.

A very normal standard version is:

Pyydän sinua auttamaan minua.

In everyday spoken Finnish, people often use colloquial pronouns:

Mä pyydän sua auttamaan mua.

Also, if the goal is simply to ask for help politely, Finnish often prefers a softer question such as:

Voisitko auttaa minua?
= Could you help me?

So your sentence is correct, but depending on context, a Finn might choose a different wording for a more natural request.