Min søster siger, at hendes muskler bliver mindre stive, efterhånden som hun træner mere regelmæssigt.

Because søster is a singular common-gender noun, and Danish possessives change with gender and number:

• min
  • singular common gender: min søster
• mit
  • singular neuter: mit hus
• mine
  • plural: mine søstre

So min søster is the correct form.

They mark the beginning of subordinate clauses.

In this sentence:

• at hendes muskler bliver mindre stive is a subordinate clause after siger
• efterhånden som hun træner mere regelmæssigt is another subordinate clause

A useful thing to know: in modern Danish, the comma before a subordinate clause is often optional if you use the no-start-comma system. So you may also see:

Min søster siger at hendes muskler bliver mindre stive efterhånden som hun træner mere regelmæssigt.

Both styles are used, but you should be consistent within a piece of writing.

Here at introduces a content clause, like English that:

• Min søster siger, at ...
• My sister says that ...

In standard written Danish, at is very normal here. In casual speech, it may sometimes be omitted, but learners should usually include it.

This is a very common Danish question.

Sin/sit/sine is used when the possessor refers back to the subject of the same clause.

But in the clause:

at hendes muskler bliver mindre stive

the subject is muskler, not hun. So the reflexive possessive sine cannot be used here.

That is why Danish uses hendes:

• hendes muskler = her muscles

Compare:

• Hun træner sine muskler. = She trains her own muscles.
  Here the subject is hun, so sine works.

But:

• Hendes muskler bliver mindre stive.
  Here the subject is muskler, so Danish uses hendes, not sine.

Because bliver shows a change.

• bliver mindre stive = become less stiff / get less stiff
• er mindre stive = are less stiff

The sentence describes improvement over time, so bliver is the natural choice.

Because stive agrees with the plural noun muskler.

With predicate adjectives after verbs like være and blive, Danish still shows agreement:

• en muskel bliver stiv
• et led bliver stift
• muskler bliver stive

So since muskler is plural, the adjective is stive.

Yes. Efterhånden som is best understood as a fixed expression meaning something like:

• as
• as gradually
• increasingly as

It introduces a process that develops at the same time as something else.

So:

efterhånden som hun træner mere regelmæssigt
means roughly:

as she trains more regularly
or
as, over time, she trains more regularly

Also note:

• efterhånden by itself often means gradually or little by little
• efterhånden som is a set phrase introducing a clause

Because regelmæssigt is an adverb here. It describes how she trains.

• hun træner regelmæssigt = she trains regularly
• hun træner mere regelmæssigt = she trains more regularly

Danish often forms the comparative of longer adverbs with mere rather than a short -ere form.

So:

• regelmæssigt = regularly
• mere regelmæssigt = more regularly

Because this is a subordinate clause, and Danish word order changes in subordinate clauses.

After a conjunction like som, at, fordi, etc., Danish normally keeps the subject before the finite verb:

• som hun træner mere regelmæssigt

In a main clause, Danish often uses verb-second word order, which can cause inversion:

• Nu træner hun mere regelmæssigt.

But after som, no inversion is needed:

• som hun træner ...
• not som træner hun ...

Because Danish uses the simple present for many things that English might express with either the simple present or a progressive form.

Here hun træner mere regelmæssigt means she trains more regularly as a current habit or pattern.

Likewise:

• siger = says
• bliver = becomes / is becoming
• træner = trains / is training, depending on context

Danish does not use a progressive form as much as English does.

Because the sentence is comparing the degree of stiffness, not the number of muscles.

• mindre stive = less stiff
• færre muskler = fewer muscles

So:

• mindre is used for amount or degree
• færre is used for countable things

Here the muscles are not becoming fewer. They are becoming less stiff.

Stivere means stiffer, so it would mean the opposite direction.

• mindre stive = less stiff
• mere stive or stivere = stiffer / more stiff

So stivere would not fit the meaning of this sentence.