Mijn opa is ouder dan mijn oom.

Because ouder is the comparative form of oud.

• oud = old
• ouder = older

Dutch usually forms the comparative by adding -er to the adjective, just like English often adds -er:

• jong → jonger = young → younger
• groot → groter = big → bigger
• oud → ouder = old → older

So in a sentence with dan (than), you normally need the comparative form:

• Mijn opa is ouder dan mijn oom.

Here, dan means than.

It is used in comparisons:

• ouder dan = older than
• groter dan = bigger than
• sneller dan = faster than

So the pattern is:

[subject] + [form of zijn] + [comparative adjective] + dan + [thing/person compared]

Example:

• Hij is langer dan ik. = He is taller than me.

Do not confuse this with als, which is used in equal comparisons:

• Hij is even oud als ik. = He is as old as me.

Because Dutch main clauses usually follow the V2 rule: the finite verb comes second.

In this sentence:

• Mijn opa = subject
• is = finite verb
• ouder dan mijn oom = rest of the sentence

So the structure is:

Mijn opa | is | ouder dan mijn oom

This is very typical Dutch word order. Even if you begin with something else, the finite verb still usually stays in second position:

• Vandaag is mijn opa ouder dan mijn oom.

Because both nouns need their own possessive word here:

• mijn opa = my grandpa
• mijn oom = my uncle

Dutch normally does not leave out the second possessive in a sentence like this. So:

• Mijn opa is ouder dan mijn oom. = correct

Leaving out the second mijn would sound incomplete or unnatural in standard Dutch.

This is similar to English, where you would also normally say my grandpa and my uncle, not my grandpa is older than uncle.

Opa means grandpa or granddad.

It is the normal everyday word and is very common. It is not rude; it is warm and natural.

A more formal or dictionary-style word is:

• grootvader = grandfather

In real life, people say opa much more often than grootvader.

So:

• mijn opa = my grandpa
• mijn grootvader = my grandfather

Because mijn already functions as the determiner, just like my in English.

Compare:

• de opa = the grandpa / the grandfather
• mijn opa = my grandpa

You do not combine mijn with de here. So:

• mijn opa = correct
• de mijn opa = incorrect

The same is true for oom:

• mijn oom = my uncle

It can mean both, just like English uncle.

So oom may refer to:

• your parent’s brother
• your aunt’s husband
• sometimes even a family friend in a more informal or childlike context, depending on the family

In this sentence, mijn oom simply means my uncle.

A rough pronunciation guide is:

• mijn ≈ similar to English mine
• opa ≈ OH-pah
• is ≈ iss
• ouder ≈ something like OW-dur or OW-der
• dan ≈ dahn
• oom ≈ a long ohm

A few useful notes:

• ou in Dutch often sounds a bit like ow in now
• oo in oom is a long o sound
• The r in ouder may sound different depending on the region

Yes, you could say:

• Mijn grootvader is ouder dan mijn oom.

This is grammatically correct and means the same thing. However, it sounds more formal, less conversational, and less personal than opa.

In everyday speech, most people would prefer:

• Mijn opa is ouder dan mijn oom.

So both are correct, but opa is more natural in ordinary conversation.

Yes, but the sentence you were given is the most neutral and natural version.

Standard order:

• Mijn opa is ouder dan mijn oom.

You can move another element to the front in Dutch, but then the verb still stays in second position. For example:

• Dan is mijn opa ouder dan mijn oom.
  This would only work in a special context and means something more like In that case, my grandpa is older than my uncle.

So for a simple statement, the original order is the best one to learn first.

Normally, no.

In:

• Mijn opa is ouder dan mijn oom.

both opa and oom stay lowercase because they are common nouns.

You would only capitalize them in special cases, such as:

• at the beginning of a sentence
• when used like a name in direct address

Example:

• Opa, kom eens hier! = Grandpa, come here!

So in your sentence, lowercase is correct.