Learn Hardcore Chinese: Tā xǐhuan chuān hóngsè de yīfu.

的 (de) links an attributive (modifier) to a noun. Here it turns the color term 红色 into a modifier of 衣服, giving 红色的衣服 “red clothes.”
Quick contrast of the three “de” particles:

的: attributive/possessive (她的衣服; 红色的衣服)
地: adverbial marker before verbs (慢慢地走 “walk slowly”)
得: complement marker after verbs/adjectives (走得很快 “walk very fast”)

Can I drop 的 and say 红色衣服 or 红衣服?

红色的衣服 is always correct and common.
红衣服 (using the adjective 红) is also natural in speech.
红色衣服 (omitting 的) is acceptable, more concise/formal; you’ll see it in headlines or written style.
If context already makes “clothes” clear, you can say 红的 (“the red one(s)”): 她喜欢穿红的.

What’s the difference between 她喜欢穿红色的衣服 and 她喜欢红色的衣服?

她喜欢穿红色的衣服: she likes to wear red clothes (preference for the action/habit).
她喜欢红色的衣服: she likes red clothes (as things), not necessarily saying she wears them.

Is it normal that 喜欢 is followed by another verb?

Yes. Pattern: 喜欢 + 动词 means “like to do (something).”
Examples:

我喜欢看书。
他不喜欢吃辣的。
喜欢 can also take a noun: 我喜欢音乐.

How is tense expressed here? Does it mean liked/likes/will like?

Chinese doesn’t mark tense on the verb. 她喜欢穿… defaults to a general/habitual statement. You can add time/frequency words:

现在她很喜欢穿红色的衣服。
她常常穿红色的衣服。
以前她不喜欢，现在喜欢了 (change of state).

Should I use 穿 or 戴 for “wear”?

穿: clothes, pants, shoes, socks (穿衣服/裤子/鞋/袜子)
戴: accessories (戴帽子/眼镜/手套/首饰)
系/繫: things you tie (系领带/腰带)
背: carry on the back (背包)

Is 衣服 singular or plural? How do I say “a piece of clothing”?

Chinese nouns don’t mark plural by form. 衣服 can mean “clothes/clothing” in general. Use measure words for counting:

一件红色的衣服 (a red piece of clothing/top)
两件红色的衬衫 (two red shirts)
一条红色的裤子 (a pair of red pants)
一双红色的鞋 (a pair of red shoes)
Don’t add 们 to inanimate nouns like 衣服.

Is 喜欢 pronounced xǐhuān or xǐhuan?

It’s xǐhuan: the second syllable is neutral tone (轻声). You will hear xǐ-huan, not xǐ-huān.

How do you pronounce 衣服? Does the 一 tone change here?

衣服 is yīfu (first tone + neutral). This 衣 is not the numeral “one,” so the tone-change rule for 一 (yī → yí/yì) does not apply.

Why is the color before the noun? Can I say “the clothes are red” instead?

Modifiers come before the noun: 红色的衣服.
To predicate a quality, use a sentence like: 衣服是红色的。 (The clothes are red.)

Can I use 爱 instead of 喜欢 here?

爱穿 is common in colloquial Mandarin and often means “tend to / have the habit of wearing,” sometimes stronger than 喜欢.

她爱穿红色的衣服 (she tends to wear red)
她很喜欢穿红色的衣服 (she really likes wearing red)
Both are okay; 喜欢 is neutral; 爱 can sound stronger or more habitual depending on context.

What’s the difference between 穿, 穿着, and 穿上?

穿: wear/put on (general).
穿着: emphasizes the state of being dressed in something (她穿着红色的衣服站在门口).
穿上: result “put something on successfully/now on the body” (她穿上红色的外套就出门了).
In your sentence, 喜欢穿 is the most natural.

How do I turn this into a yes–no question or a negative?

Yes–no (吗): 她喜欢穿红色的衣服吗？
A-not-A: 她喜不喜欢穿红色的衣服？
Negative: 她不喜欢穿红色的衣服。

Where do 也 and 都 go if I want “also” or “all”?

Also: 她也喜欢穿红色的衣服。
All/both: 她们都喜欢穿红色的衣服。
也/都 typically come before the verb phrase.

Do I need 很 before 喜欢 like I often see before adjectives?

Not required. 很 is often used before adjectives as a neutral linker (她很高). With verbs like 喜欢, 很 adds emphasis:

她喜欢穿红色的衣服 (neutral)
她很喜欢穿红色的衣服 (really likes)

What’s the difference between 红 and 红色?

红 is an adjective “red.”
红色 is the noun “the color red” used attributively.
Both can modify nouns: 红衣服 or 红色的衣服. 红色 tends to sound a bit more formal/explicit as a color term.

How do I specify “the red one” or “that red piece of clothing”?

“the red one(s)” (clothes implied): 红的
“that red one”: 那件红色的衣服
“these red ones”: 这些红色的衣服

How could I say “She prefers wearing red clothes (to blue ones)”?

她更喜欢穿红色的衣服（而不是蓝色的）。
她比较喜欢穿红色的衣服。 (softer “rather like”)