Hän tulee tietenkin mukaan.

Hän can mean either he or she. Finnish does not normally mark gender in third-person singular pronouns.

So:

• hän = he / she
• the exact gender usually comes from context

This is a very common thing for English speakers to notice, because English forces you to choose between he and she, but Finnish does not.

Tulee is the third-person singular present tense form of the verb tulla, which means to come.

So:

• tulla = to come
• hän tulee = he/she comes, he/she is coming, or sometimes he/she will come, depending on context

This is the normal form used with hän.

It can mean any of those, depending on context.

Finnish often uses the present tense where English might use either:

• comes
• is coming
• will come

So Hän tulee tietenkin mukaan could be understood as:

• He/She is of course coming along
• He/She will of course come along
• He/She of course comes along

In real use, the surrounding situation tells you which time meaning is intended.

Tietenkin is an adverb meaning of course, naturally, or obviously.

It adds the speaker’s attitude: the speaker thinks this is expected or unsurprising.

In this sentence, it tells us that the person’s coming along is something the speaker sees as obvious.

They are very close in meaning. Both usually mean of course.

In many situations, they are interchangeable:

• Hän tulee tietenkin mukaan.
• Hän tulee tietysti mukaan.

Both sound natural. There can be small differences in tone depending on speaker and context, but for a learner, it is safe to treat them as near-synonyms.

Historically, yes, it is related, but as a learner it is best to treat tietenkin as a fixed whole meaning of course.

In other words:

• do not try to build the meaning piece by piece every time
• learn tietenkin as one common adverb

That will be much more useful than over-analyzing it.

Mukaan means something like along, with, or joining in.

In this sentence, it means the person is coming along with the group or joining the others.

So tulla mukaan is a very common combination:

• to come along
• to come with
• to join

This is one of the most useful everyday expressions in Finnish.

This is an important distinction.

• mukaan usually has a sense of movement toward joining
• mukana usually describes a state of being along / being included / being present

Compare:

• Hän tulee mukaan. = He/She comes along.
  -> movement into the group
• Hän on mukana. = He/She is along / is involved / is included.
  -> state, no movement

Because the verb is tulee (comes), mukaan is the natural choice.

Finnish often leaves that part understood from context.

So Hän tulee mukaan already suggests:

• joining us
• coming with the others
• coming along with the group already being discussed

If needed, Finnish can make it explicit, for example:

• Hän tulee meidän mukaan. = He/She is coming with us.
• Hän tulee heidän mukaan. = He/She is coming with them.

But very often, just mukaan is enough.

No, Finnish word order is fairly flexible, though some orders are more neutral than others.

Hän tulee tietenkin mukaan is a very natural, neutral order.

You could also say:

• Tietenkin hän tulee mukaan.
  -> emphasizes of course
• Hän tietenkin tulee mukaan.
  -> also natural, slightly different focus

So the sentence can be rearranged, but the version you were given is a basic and normal one.

Yes. In spoken Finnish, people often use se instead of hän when talking about a person, especially in informal conversation.

So in everyday speech you might hear:

• Se tulee tietenkin mukaan.

You might also hear tietysti instead of tietenkin:

• Se tulee tietysti mukaan.

In standard written Finnish, though, hän is the normal form for a person, so Hän tulee tietenkin mukaan is a good standard sentence to learn.