Mi hija marca con el subrayador lo que debe aprender de memoria.

All three can work, but they’re not equally specific.

• marcar = “to mark.” It’s generic (tick, mark, dial, score). It can cover “highlight,” but it’s less specific.
• subrayar = “to underline.” Many people also use it loosely for highlighting text.
• resaltar = “to highlight” (both literally and figuratively) and is very common in Latin America.

More idiomatic options for Latin America:

• Mi hija resalta lo que debe aprender de memoria.
• Mi hija subraya lo que debe aprender de memoria.

All three mean “highlighter,” with regional preferences:

• resaltador: very common across Latin America.
• marcatextos: very common in Mexico.
• subrayador: widely understood, but more frequent in Spain; you’ll still hear it in Latin America.

Your sentence is understood as-is everywhere, but in Latin America many would naturally say resaltador or (in Mexico) marcatextos.

You can omit it if the context already makes the tool obvious:

• With tool: Mi hija resalta con el resaltador lo que debe aprender de memoria.
• Without tool: Mi hija resalta lo que debe aprender de memoria.

Both are possible. Use:

• el subrayador when a specific highlighter is implied (the one she uses).
• un subrayador when you mean any highlighter or you’re introducing it for the first time.

lo que = “what / that which.” It’s a neuter relative pronoun used when there’s no explicit antecedent. So lo que debe aprender de memoria = “what she has to memorize.” If you had a clear antecedent, you’d agree with it:

• las partes que debe aprender (feminine plural antecedent, e.g., “las partes”)
• With no antecedent, use neuter lo que.

qué is interrogative/exclamative (“what?”), used in direct or indirect questions. Here we’re not asking a question; we’re referring to unspecified things. So:

• Correct: Marca lo que debe aprender…
• Question: ¿Marca qué debe aprender…? (a direct question)
• Indirect question: No sé qué debe aprender.

Both mean “has to,” but there’s a nuance:

• deber + infinitive can suggest duty/obligation or strong advice (often a bit more formal).
• tener que + infinitive is the most neutral/colloquial way to say “have to.” Either works here:
• …lo que debe aprender de memoria.
• …lo que tiene que aprender de memoria.

Indicative (debe) is used because the items to memorize are taken as known/real/specific. Use subjunctive (deba) if what she’ll have to memorize is unknown, hypothetical, or viewed generically/prospectively:

• Known set: Marca lo que debe aprender.
• Indefinite/generic: Marca lo que deba aprender (whatever she may have to learn).

All are fine:

• aprender de memoria: very common and natural.
• memorizar: a bit more formal/technical but perfectly correct.
• aprenderse de memoria: reflexive; also very common, often implying thoroughness.
• After memorizing, you can say saberse algo de memoria (“to know something by heart”).

Spanish is a pro‑drop language; the verb ending already tells you the subject. (Ella) debe both mean “she must,” but ella is only added for emphasis, contrast, or clarity:

• Neutral: Mi hija debe…
• Emphasis/contrast: Ella debe…, no su hermano.

Yes. Spanish allows flexible word order for adjuncts:

• Mi hija marca con el subrayador lo que debe aprender de memoria.
• Mi hija marca lo que debe aprender de memoria con el subrayador. Put it where it sounds clearest and least heavy.

Spanish simple present covers habitual actions. Use the progressive only for an action happening right now:

• Habit: Mi hija marca… (“My daughter highlights [as a routine].”)
• Right now: Mi hija está marcando…