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Now for the question about "macht".
One of the very first things you will learn about German language, is that all noun are always written with an uppercase first letter. Always! There are no exceptions. Other words are capitalized only if they are the first word of a sentence (like in English.) So, "Macht" and "macht" are two very different words. Both of them exist:
Macht
The first letter of this word is an uppercase letter, so it's a noun. Like almost all words in almost all languages is has more than just one meaning. Here are some meanings:
- power, authority, strength, influence
Mein Chef hat die Macht, mir mein Gehalt zu kürzen.
My boss has the power to cut my salary.
- state, regency, leadership
Deutschland ist eine wichtige Macht in Europa.
Germany is an important power in Europe.
Note, that the English word "power" has even more meanings. But they do not translate to German "Macht", like in physics (electrical power = German "Strom") or mathematics (the third power of x = "die dritte Potenz von x")
macht
The first letter of this word is a lowercase letter, so it's not a noun. It is something else. The word "macht" is a grammatical form of the verb "machen", which can be translated into English as "to do" or "to make" (plus more than 10 other possibilities, depending on the meaning).
The word "macht" is:
- Third person singular indicative present active of "machen"
Georg macht Hüte. Jürgen macht immer solche Sachen.
George makes hats. Jürgen always does things like this.
- Second person singular indicative present active of "machen"
Ihr beide macht Hüte. Ihr beide macht immer solche Sachen.
You both make hats. You both always do things like this.
- Second person singular indicative imperative present active of "machen"
Macht jetzt endlich Hüte! Macht jetzt mal solche Sachen!
Now finally make hats! Do things like this now!
The verb machen has many different meanings. Wiktionary lists 21 different meanings. I'm not going to explain all of them here. And the verb tun also has a lot different meanings. And also the englisch verbs make and do have lots of different meanings. And sometimes it is better to translate machen as make, but sometimes do fits better, and in other situation even other verbs might fit better. And this is true for tun too.
Generally spoken, if you want to express that something is created or built, then you have machen = to make:
Georg macht Hüte. = Georg makes hats.
But if you want to express, that someone performs an action, you have machen = to do:
Kann bitte jemand die Tische abwischen? - Ja, klar, ich mache das gerne.
Can someone wipe down the tables, please? - Yeah, sure, I'll be happy to do it.
The words "tun" and "leid" in the phrase »das tut mir leid« behave like one semantic unit. They strongly belong together. In English there is no similar grammatical construction, so you have to express the same meaning using another grammatical pattern, and the best English version is "I'm sorry" which again is a pattern that doesn't exist in German.
Note, that you never translate words! What you have to translate are meanings!