Как ни красива эта ромашка, мне всё равно больше нравится красный тюльпан.

Here как ни introduces a concessive idea: no matter how..., however..., or as ... as ... may be.

So:

• Как ни красива эта ромашка...
  = No matter how beautiful this daisy is...
  = However beautiful this daisy is...

This is a common literary or slightly elevated pattern in Russian:

• Как ни старайся, ничего не выйдет.
  = No matter how hard you try, nothing will work out.
• Как ни интересно, времени нет.
  = However interesting it is, there’s no time.

So the first part sets up a contrast: even granting that the daisy is very beautiful, the speaker still prefers the red tulip.

Красива is the short form of the adjective красивая.

Russian has two adjective forms in many cases:

• long form: красивый / красивая / красивое / красивые
• short form: красив / красива / красиво / красивы

In this sentence, the adjective is used predicatively, meaning it functions like is beautiful, not like a beautiful daisy.

Compare:

• красивая ромашка = a beautiful daisy
  adjective directly modifies the noun
• ромашка красива = the daisy is beautiful
  short form used as the predicate

So Как ни красива эта ромашка... literally has the structure However beautiful this daisy is...

The short form is especially common in more formal, literary, or expressive styles.

Because эта ромашка is the subject of the clause.

The structure is basically:

• эта ромашка красива = this daisy is beautiful

In Russian, the verb to be in the present tense is usually omitted, so there is no visible is. But grammatically, эта ромашка is still the subject, so it stays in the nominative.

That is why you get:

• эта ромашка — nominative subject
• красива — short-form adjective meaning beautiful

Here всё равно means all the same, anyway, still, or nevertheless.

So:

• мне всё равно больше нравится красный тюльпан
  = I still like the red tulip more
  = All the same, I prefer the red tulip

Important: in other contexts, всё равно can also mean it makes no difference or I don’t care, but that is not the meaning here.

Compare:

• Мне всё равно.
  = I don’t care / It makes no difference to me.

But in your sentence, it strengthens the contrast:

• However beautiful this daisy is, I still prefer the red tulip.

Russian often expresses liking with the verb нравиться, which works differently from English to like.

Literally, нравиться means something like:

• to be pleasing to

So:

• мне нравится тюльпан
  literally = the tulip is pleasing to me
  natural English = I like the tulip

That is why:

• мне is in the dative case = to me
• красный тюльпан is the grammatical subject

By contrast, любить usually means to love, and it is often stronger than English like:

• Я люблю тюльпаны. = I love tulips.

So нравится is the natural choice for I like / I prefer in this sentence.

Because the grammatical subject is красный тюльпан, which is singular.

With нравиться, the verb agrees with the thing that is pleasing, not with the person in мне.

So:

• Мне нравится красный тюльпан.
  = I like the red tulip.
• Мне нравятся красные тюльпаны.
  = I like red tulips.

In your sentence, the subject is:

• красный тюльпан — singular masculine

So the verb must be:

• нравится — singular

Yes, in many contexts больше нравится is a natural way to express prefer.

Literally:

• больше нравится = is liked more

So:

• Мне больше нравится красный тюльпан.
  literally = The red tulip pleases me more.
  natural English = I prefer the red tulip.

Russian often uses this pattern instead of a separate verb meaning prefer in everyday speech.

You may also see:

• Я предпочитаю красный тюльпан.
  = I prefer the red tulip.

But мне больше нравится... often sounds more conversational and less formal.

Because with нравиться, the thing liked is the subject of the sentence.

So in:

• мне больше нравится красный тюльпан

the roles are:

• мне = to me (dative)
• красный тюльпан = the red tulip (subject, nominative)
• нравится = is pleasing

This often feels backwards to English speakers, because English says:

• I like the red tulip

But Russian structures it more like:

• The red tulip is pleasing to me

That is why красный тюльпан is nominative, not accusative.

Because Russian often leaves the comparison understood from context.

The first clause already mentions the daisy:

• Как ни красива эта ромашка...

Then the second clause says:

• мне всё равно больше нравится красный тюльпан

So the full implied meaning is:

• I still like the red tulip more than this daisy

Russian does not need to repeat чем эта ромашка if it is already obvious.

If you wanted to make it fully explicit, you could say:

• Как ни красива эта ромашка, мне всё равно больше нравится красный тюльпан, чем она.

But that is less elegant here, because the comparison is already clear.

Yes, the word order is natural and stylistically smooth.

Russian word order is flexible, and here the sentence is arranged to emphasize the contrast:

1. Как ни красива эта ромашка — concession first
2. мне всё равно больше нравится красный тюльпан — main point after it

This creates the effect:

• Even though the daisy is beautiful, my real preference is still the red tulip.

You could rearrange parts of the second clause, for example:

• ...мне больше всё равно нравится красный тюльпан — awkward
• ...красный тюльпан мне всё равно нравится больше — possible, with different emphasis
• ...мне нравится больше красный тюльпан — possible, but less neutral

The original version is very natural because it builds up neatly to the contrasted item красный тюльпан.

Yes, ромашка can refer to what English speakers may call daisy or chamomile, depending on context.

In everyday usage, ромашка often brings to mind the familiar white flower with a yellow center. In translations, it is often rendered as daisy, though botanically the match is not always exact.

So in a learner’s sentence like this, daisy is a very natural translation.

The important point grammatically is that ромашка is:

• feminine
• singular
• nominative here

That is why you get:

• эта ромашка
• красива

Both agree with a feminine singular noun.