Learn Hardcore German: Ich bin froh, Sie heute persönlich kennenzulernen und Ihre Fragen zum Sprachkurs beantworten zu können. - I am glad to get to know you personally today and to be able to answer your questions about the language course.

It always takes a capital letter, no matter where it appears in the sentence.
In this sentence, Sie is the direct object of kennenzulernen – it means “to get to know you / to meet you” (politely).
It does not mean “she” here (that would be sie with a small s, and the verb form would look different in a full clause).

So Sie kennenzulernen = “to meet you (formal)”.

Why is it Ihre Fragen with a capital I, and what case is Ihre Fragen in?

Ihre with a capital I is the possessive form of the formal Sie (“you”).

Ihr(e) normally means “her” or “their”, but when it’s capitalized (Ihr / Ihre), it means “your” (formal).
Ihre Fragen = “your questions” (talking politely to one person or several people).

Grammatically:

Fragen is the direct object of beantworten (to answer), so it is in the accusative plural.
The article/possessive must match: Ihre (feminine plural form) + Fragen (plural) → Ihre Fragen.

What is the structure Ich bin froh, ... zu ... doing here? Why is zu used?

The pattern is:

Ich bin froh, + [zu + infinitive]
= “I am glad to …”

Ich bin froh, Sie kennenzulernen literally: “I am glad, to-get-to-know you.”
German often uses zu + infinitive after certain adjectives (like froh, glücklich, bereit, schwer, etc.).

So:

Main clause: Ich bin froh = “I am glad”
Infinitive clause: Sie heute persönlich kennenzulernen und Ihre Fragen … beantworten zu können
The infinitive clause explains what the speaker is glad about.

Why is kennenzulernen written with zu in the middle and not just zu kennenlernen?

kennenlernen is a verb with a separable prefix:

In the normal present tense: Ich lerne Sie kennen. (prefix kennen goes to the end)
The infinitive form is kennenlernen (written as one word in modern spelling).

With zu, separable-prefix verbs put zu in the middle:

kennenlernen → kennenzulernen
aufmachen → aufzumachen
anrufen → anzurufen

So Sie kennenzulernen is the correct zu + infinitive form.

What’s the difference between kennenlernen and just treffen or kennen?

They are related but not identical:

kennenlernen = “to get to know (for the first time) / to meet (for the first time)”
- Ich freue mich, Sie kennenzulernen. = “I’m happy to meet you (for the first time).”
treffen = “to meet” in the sense of meeting someone (often intentionally), not necessarily for the first time.
- Ich treffe ihn morgen. = “I’m meeting him tomorrow.”
kennen = “to know (be acquainted with) someone/something.”
- Ich kenne ihn. = “I know him.”

So here kennenzulernen is appropriate because it’s a first or introductory meeting.

Why is it beantworten and not just antworten after Ihre Fragen?

German distinguishes these two verbs:

antworten (jemandem) = to answer someone (dative person, no direct object)
- Ich antworte Ihnen. = “I answer you.”
beantworten (etwas) = to answer something (accusative thing)
- Ich beantworte Ihre Fragen. = “I answer your questions.”

Since Fragen (questions) is the thing being answered, beantworten is correct:

Ihre Fragen beantworten = “to answer your questions.”

What is the role of zu können in Ihre Fragen … beantworten zu können? Why not just Ihre Fragen … zu beantworten?

können is a modal verb meaning “can / to be able to.”

Ihre Fragen beantworten = “to answer your questions.”
Ihre Fragen beantworten können = “to be able to answer your questions.”

With zu + infinitive and a modal verb, German puts zu in front of the last verb:

beantworten können → beantworten zu können
helfen können → helfen zu können

So Ihre Fragen … beantworten zu können = “to be able to answer your questions.”

It expresses ability / possibility, not just the bare action.

Why is the sentence not … und ich kann Ihre Fragen beantworten, but uses this long … und Ihre Fragen … beantworten zu können structure instead?

Both are grammatically possible but not stylistically equivalent:

Ich bin froh, Sie … kennenzulernen und ich kann Ihre Fragen beantworten.
- This has two separate clauses: “I am glad … and I can answer your questions.”
- It states ability as a separate fact, not as part of what makes the speaker glad.
Ich bin froh, Sie … kennenzulernen und Ihre Fragen … beantworten zu können.
- Both actions are part of one infinitive construction linked to Ich bin froh.
- It means: “I am glad [to meet you and (to) be able to answer your questions].”

So the original version more tightly links both actions to “being glad” and sounds smoother and more formal.

Why is there a comma after Ich bin froh?

The comma separates the main clause from the infinitive clause:

Main clause: Ich bin froh (“I am glad”)
Infinitive clause: Sie heute persönlich kennenzulernen und Ihre Fragen … beantworten zu können

In German, an infinitive clause with zu is normally set off by a comma, especially when it depends on a verb or adjective like froh, bereit, versuchen, etc.

So the comma is required:
Ich bin froh, Sie … kennenzulernen …

Why is the order Sie heute persönlich kennenzulernen and not Sie persönlich heute kennenzulernen?

German tends to follow the time–manner–place order for adverbials. Here:

heute = time (today)
persönlich = manner (personally, in person)

So heute persönlich follows the usual pattern:

Sie heute persönlich kennenzulernen = “to meet you personally today.”

Other orders are possible and not always wrong, but heute persönlich is the most neutral-sounding order here.

What does zum Sprachkurs literally mean, and why not über den Sprachkurs?

zum = contraction of zu dem.

Literally:

Fragen zum Sprachkurs = “questions to the language course”

But idiomatically it means “questions about the language course.”

Both are possible in German:

Fragen zum Sprachkurs (more compact, very common)
Fragen über den Sprachkurs (“questions about the language course”)

Here zum sounds very natural and is often preferred in this kind of phrase.

Is there a difference between Ich bin froh, Sie kennenzulernen and Ich freue mich, Sie kennenzulernen?

They are very close in meaning and both are common.

Ich bin froh, Sie kennenzulernen.
- Slightly more factual, like “I am glad to meet you.”
Ich freue mich, Sie kennenzulernen.
- Slightly more personal / emotional, like “I’m pleased / I’m looking forward to meeting you.”

In everyday polite conversation (for example, first meetings), Ich freue mich, Sie kennenzulernen is extremely common, but Ich bin froh, … is also correct and polite.