Dudo que la picadura de mosquito haya causado tanta hinchazón por sí sola.

Because the main verb is dudo (I doubt), and expressions of doubt typically trigger the subjunctive in Spanish.

So:

• Dudo que... → doubt / uncertainty → subjunctive
• Creo que... → belief / certainty → usually indicative

That is why Spanish says:

• Dudo que la picadura... haya causado...

and not:

• Dudo que la picadura... ha causado... ❌

The speaker is not presenting the cause as a fact, but as something uncertain.

Haya causado is the present perfect subjunctive.

It is formed like this:

• haya = subjunctive of haber
• causado = past participle of causar

This tense is used when the speaker is talking about a past action that is still relevant now. In this sentence, the swelling is clearly still being discussed in the present, so the past cause is connected to a current result.

So the idea is:

• I doubt that the mosquito bite has caused / could have caused so much swelling on its own.

If you used cause (present subjunctive), it would sound more like a present/future possibility:

• Dudo que la picadura de mosquito cause tanta hinchazón.
  = I doubt the mosquito bite causes / will cause that much swelling.

That version is also possible, but it is slightly different in meaning.

Yes, but it would shift the time perspective.

• Dudo que ... haya causado ... = I doubt it has caused it
  → the doubt is connected to the present situation
• Dudaba que ... hubiera causado ... = I doubted it had caused it
  → the doubt is placed in the past

You would normally match the tense of the main verb and the subordinate verb:

• Dudo que ... haya causado ...
• Dudaba que ... hubiera causado ...

So in your sentence, haya causado is the natural choice because dudo is in the present.

Because que introduces a subordinate clause, just like that in English:

• Dudo que... = I doubt that...

Spanish uses que very often to link clauses after verbs of thinking, saying, believing, doubting, wanting, etc.

Examples:

• Creo que viene. = I think that he’s coming.
• Espero que venga. = I hope that he comes.
• Dudo que venga. = I doubt that he’s coming / will come.

Even though English often drops that, Spanish normally keeps que.

Because de mosquito here means a mosquito bite in a general, type-of-thing sense, not the bite of a specific mosquito.

Compare:

• la picadura de mosquito = a mosquito bite / mosquito bite
• la picadura del mosquito = the bite of the mosquito (a specific mosquito already identified)

So de + noun without an article often works like an English noun used attributively:

• gafas de sol = sunglasses
• cepillo de dientes = toothbrush
• picadura de mosquito = mosquito bite

It describes the kind of bite.

For the same reason: de mosquito is functioning as a type label, not referring to one specific mosquito.

Spanish often leaves out the article after de when the second noun identifies the type or category:

• zumo de naranja = orange juice
• tienda de ropa = clothes shop
• picadura de mosquito = mosquito bite

If you said de un mosquito, that would mean from a mosquito, with more emphasis on one individual mosquito. That is grammatical, but less natural here.

Because tanto/tanta/tantos/tantas is used before nouns, while tan is used before adjectives and adverbs.

Here, hinchazón is a noun, so you need tanta:

• tanta hinchazón = so much swelling

Compare:

• tan grande = so big
• tan rápidamente = so quickly
• tanta hinchazón = so much swelling
• tantos problemas = so many problems

Also, hinchazón is feminine singular, so the form is tanta.

Because here hinchazón is being treated as an uncountable idea, like swelling in English.

The sentence is talking about the overall amount of swelling, not several separate swellings. That is why singular sounds natural:

• tanta hinchazón = so much swelling

You could use the plural hinchazones in other contexts, but that would usually mean distinct swellings in different places or episodes of swelling.

It means by itself, on its own, or alone.

In this sentence, it means:

• the mosquito bite alone is probably not enough to explain that much swelling

So the implication is that there may be some other factor involved, such as:

• an allergic reaction
• infection
• another cause

This expression is very common in Spanish:

• por sí solo / sola = by itself / on its own

Examples:

• Eso no explica el problema por sí solo.
• La medicina por sí sola no basta.

Because sola agrees with the thing it refers to, which is la picadura.

• la picadura = feminine singular
• therefore: por sí sola

Agreement changes depending on the noun:

• el medicamento por sí solo
• la picadura por sí sola
• los síntomas por sí solos
• las pastillas por sí solas

So the feminine form is required here.

In por sí sola, sí is a stressed pronoun meaning something like itself / himself / herself / themselves, depending on context.

It has an accent to distinguish it from si without an accent:

• sí = self / yes
• si = if

So:

• por sí sola = by itself
• si viene = if he/she comes

The accent helps show that this is the pronoun sí, not the conjunction si.

Yes. Both are possible, but they feel slightly different.

• Dudo que la picadura de mosquito...
  sounds like the mosquito bite already known in the situation
• Dudo que una picadura de mosquito...
  sounds more general: I doubt a mosquito bite would/could...

So:

• la = the specific bite we are talking about
• una = any mosquito bite / a mosquito bite in general

In your sentence, la suggests the speaker is referring to a particular bite the listener already knows about.

Dudo que is very natural. But Spanish has several similar options, each with a slightly different tone:

• Dudo que... = I doubt that...
• No creo que... = I don’t think that...
• No me parece que... = It doesn’t seem to me that...
• Me cuesta creer que... = I find it hard to believe that...

All of them would normally take the subjunctive after que.

For example:

• No creo que la picadura de mosquito haya causado tanta hinchazón por sí sola.

That is very close in meaning, but dudo que sounds a bit more direct and explicit.

Because in Spanish, insect bites and stings are often expressed with picadura.

• picadura is commonly used for bites/stings from insects such as mosquitoes
• mordedura is more typical for animals that literally bite, such as dogs or snakes

So:

• picadura de mosquito = mosquito bite
• mordedura de perro = dog bite

Even though English uses bite for mosquitoes, Spanish usually prefers picadura.

Yes, sometimes, but its position at the end is very natural and clear.

For example, these are possible:

• Dudo que la picadura de mosquito haya causado tanta hinchazón por sí sola.
• Dudo que, por sí sola, la picadura de mosquito haya causado tanta hinchazón.

The second version is more marked or emphatic. The original word order is the most neutral and natural in everyday Spanish.

Putting por sí sola at the end makes it easy to understand that it modifies la picadura de mosquito.