Hún heldur að þessi planta þurfi stærri pott, því rótin er orðin of löng.

Yes, heldur can be different things in different sentences.

Here, heldur is the 3rd person singular present form of halda, in the expression halda að, which means to think/believe that.

So:

• Hún heldur að ... = She thinks that ...

In other contexts, heldur can also mean rather. That is a different use.

Þurfi is the present subjunctive of þurfa (to need).

Icelandic often uses the subjunctive in a subordinate clause after a verb of opinion, belief, uncertainty, or reported thought. Since the sentence is saying what she thinks, not stating the need as an absolute fact, þurfi is very natural here.

• indicative: þarf
• subjunctive: þurfi

You may sometimes hear þarf in everyday speech, but þurfi is the more clearly grammatical choice in this kind of sentence.

Because þessi has to agree with planta.

• planta is a feminine singular noun
• here it is the subject of the clause, so it is in the nominative
• the matching demonstrative form is þessi

So þessi planta means this plant.

Also, when Icelandic uses a demonstrative like þessi, it normally does not add the suffixed definite article to the noun.

Because Icelandic does not have an indefinite article like English a/an.

So:

• pottur = pot
• stærri pott = a bigger pot

The idea of a is simply understood from the context.

Because pott is the accusative form, and it is the direct object of þurfa.

• nominative: pottur
• accusative: pott

Since the plant needs the pot, pot is the object, so accusative is used.

Stærri means bigger. It is the comparative form of stór (big).

This comparison is irregular:

• stór = big
• stærri = bigger
• stærstur = biggest

So stærri pott means a bigger pot.

Here því means because or since.

It introduces the reason:

• ..., því rótin er orðin of löng.
• ..., because the root has become too long.

You can think of it as a shorter way of introducing a reason clause, similar in meaning to af því að.

Rótin means the root.

The ending -in is the definite article attached to the noun:

• rót = root
• rótin = the root

Icelandic usually puts the onto the end of the noun instead of using a separate word.

Er orðin literally means something like is become, but in natural English it is usually has become or has gotten.

So:

• rótin er orðin of löng = the root has become too long

The form orðin agrees with rótin, which is feminine singular. The past participle of verða changes form to match the subject.

No. Here of means too.

So:

• of löng = too long

It is not the same as the English preposition of.
Compare:

• mjög löng = very long
• of löng = too long

Because the adjective has to agree with rótin.

The dictionary form is langur (long), but it changes by gender and case. Here the noun is feminine singular nominative, so the correct form is löng.

So:

• langur = masculine
• löng = feminine
• langt = neuter

That is why the sentence has rótin er ... löng.

Because these are subordinate clauses.

In main clauses, Icelandic often follows a verb-second pattern. But after conjunctions like að and því, the clause usually has more regular subject-verb order:

• að þessi planta þurfi ...
• því rótin er ...

So this word order is normal and expected in this sentence.