İlkbahar kısa sürse bile Nisan ve Mayıs aylarını çok seviyorum.

It comes from:

• sürmek = to last, continue
• -se / -sa = a conditional-type suffix
• bile = even

So sürse bile literally means even if it lasts.

In this sentence, İlkbahar kısa sürse bile means even if spring is short / even though spring does not last long.

Because kısa sürmek is a very common Turkish expression meaning to last a short time.

So:

• İlkbahar kısa = Spring is short
• İlkbahar kısa sürüyor = Spring lasts only a short time

In your sentence, the idea is not just that spring is short in some abstract sense, but that it doesn’t last long.

Because Turkish verbs already show the subject.

• seviyorum = I love / I am loving
• The ending -um shows I

So Turkish often leaves out ben unless it is needed for emphasis.

• (Ben) Nisan ve Mayıs aylarını çok seviyorum.

Both are possible, but without ben is more natural in many contexts.

This is one of the trickiest parts of the sentence.

Nisan ve Mayıs ayları means the months of April and May or more naturally April and May.

Here, ayları is part of a Turkish noun compound structure. In this kind of phrase, the second noun often takes a possessive-looking ending:

• nisan ve mayıs ayları = April and May (months)

Then, because this whole phrase is the direct object of seviyorum, it also gets the accusative ending:

• ayları
  • -ı → aylarını

So:

• Nisan ve Mayıs ayları = April and May
• Nisan ve Mayıs aylarını = April and May, as the definite object

Because Turkish often uses the accusative for specific/definite direct objects.

Here, the speaker is talking about specific months: April and May. That makes the object definite.

So:

• Nisan ve Mayıs aylarını seviyorum = I love April and May
• the -ı / -i / -u / -ü type ending marks that definite object

This is a very common pattern in Turkish.

That n is a buffer consonant.

The form is basically:

• ayları
  • accusative -ı

But Turkish usually inserts n between a possessive-marked noun and another suffix:

• ayları + ı → aylarını

So the n is there to make the word connect properly.

Yes.

Although -se bile is literally close to even if, in real English translation this sentence can sound more natural as:

• Although spring is short, I really love April and May.
• Even though spring doesn’t last long, I love April and May very much.

So the Turkish structure is flexible in translation.

Because in Turkish, adverbs usually come before the verb.

• çok seviyorum = I love very much / I really love

So çok is modifying the verb seviyorum.

This is very normal word order in Turkish:

• seni çok seviyorum = I love you very much

In standard Turkish, month names are usually written in lowercase:

• nisan
• mayıs

So a more standard version would be:

• İlkbahar kısa sürse bile nisan ve mayıs aylarını çok seviyorum.

Many learners ask this because English capitalizes month names, but Turkish normally does not.