Learn Hardcore Chinese: tā yòu lái wǒ jiā le, wǒ ràng tā xiān jìnlái. - He came to my place again; I asked him to come in first.

又 marks a repetition that has already happened (often with sentence-final 了): 他又来我家了 (He came again).
再 is for a future or hypothetical repetition: 他明天再来 (He’ll come again tomorrow).
Avoid using 再...了 for past events; that combination is generally wrong for this meaning.

What does the sentence-final 了 do in the first clause?

It’s the change-of-state/assertive 了, signaling a new situation: “He has (now) come again.” Without 了, 他又来我家 would read more like a habitual/general statement rather than a newly occurred event.

Why is 了 at the end instead of after 来?

With motion verbs like 来/去 that take a place complement, the perfective/change marker 了 usually goes after the whole clause:

Correct: 他又来我家了.
Odd: 他又来了我家. If you want 了 right after the verb, use 到: 他又到了我家.

Can I say 他又到我家来 or 他又来到我家? Are they different from 他又来我家了?

All are acceptable with slight stylistic differences:

他又来我家了: very common, colloquial.
他又到我家来了: emphasizes arrival to a location (到…来).
他又来到我家了: more formal/literary feel (来到 as a compound). They convey the same basic idea.

Why is it 我家 instead of 我的家?

我家 is the default, idiomatic way to say “my home/household,” especially as a location: 我家在北京.
我的家 is also correct but can sound more formal or emphatic, often treating 家 as a concrete noun: 我的家很温暖.

What exactly does 让 mean here? How is it different from 叫 and 请?

让 + 人 + VP: let/allow, have/make, or tell someone to do something (neutral; context decides the nuance).
叫 + 人 + VP: tell/order someone to do something (more directive).
请 + 人 + VP: politely invite/request.
In this sentence, 让 is a neutral “let/have him come in.”

Why is 先 placed before 进来? Can I say 我先让他进来?

我让他先进来: He goes in first (before others/other actions); 先 modifies 进来.
我先让他进来: The first thing I did was to allow him in (before doing something else); 先 modifies 让.
Both are grammatical but emphasize different “firsts.”

What’s the difference between 进来 and 进去?

进来: enter toward where the speaker is (or the deictic “here”).
进去: enter away from the speaker (into “there”).
Examples:
我在屋里：请进来。
我在屋外，对他指屋里：你先进去。

Can I drop 来 and just say 进?

Yes, 进 alone means “enter,” and you’ll hear it in brief instructions: 我让他进.
But 进来/进去 are more idiomatic in full sentences because they encode direction clearly: 我让他进来 / 我让他进去.

If I’m outside the house, what should I say?

Use 进去: 我让他先进去 (I let him go in first [away from me]).

Does 又 carry a complaining tone?

It often can, especially with 又 + V + 了 for repeated events: 他又迟到了 (He’s late again). But context matters; it can be neutral. To sound explicitly neutral or positive, add framing: 他又来我家了，这次聊得很好. You can also use 又一次 for a neutral/formal tone: 他又一次来我家了.

Why isn’t there a 了 in the second clause? Should it be 我让他先进来了?

You don’t need 了 there to show past; Chinese often marks just one clause to anchor the timeline.

我让他先进来: neutral narration; the result is understood from context.
我让他先进来了: puts 了 on the result (进来), emphasizing that he indeed ended up inside first. It’s possible but less necessary in simple narration.
Don’t put 了 after 让 here (我让了他…)—that means a different verb “to yield/give way.”

Can I say 来进 instead of 进来?

No. Directional compounds are fixed as “Verb + 来/去”: 进来, 出去, 上来, 下去, 回来, 过来. 来进 is ungrammatical.

Is 他又来了我家 acceptable?

No. Keep 了 after the whole clause with motion + place:

他又来我家了.
or use 到:
他又到我家来了.
他又来了 is fine only when no place follows.