That might be correct.
However, in the Spanish course, DUO often uses unnecessary subject pronouns, perhaps to help people learn them. Many of the native Spanish speaker point out (complain about) the unnecessary subject pronouns.
Possibly the same is happening here.
It's the same, and there's nothing to complain about. It's normal to use the pronouns in the beginning. I never saw a beginner Spanish class where they say "Hey, we don't use the pronouns, because it's less common to use them than to skip them, so you won't learn them". That makes no sense at all.
The people interested in Latin will go on their courses and reading, so they will meet the most common usages, while knowing it's not ungrammatical to use pronouns.
They essentially are. It's two ways to say basically the same thing, just as the two English phrases are. The habere phrase is a little more closely tied to your physical/mental state (just like "feeling" in English), whereas the agere phrase may invite the discussion of one's work life, etc. in place of emotions & health.
A piece of evidence for the fact that h was either mute or at least very weak, is that an initial h (= h at the start of a word) did not prevent elision, in poetry.
In other words: elision happens in poetry regularly, when a word ending in a vowel (like ille) immediately precedes a word beginning with a vowel (like et). So, in line 3 of Vergil's Aeneid Book 1, we see: ... ille et terris iactatus et alto, which would be read metrically as ... illet terris iactatus et alto.
(I didn't quote the first part of the line, because I wanted to explain first that another type of elision happens, when a syllable ending in 'vowel + m' precedes a word that starts with a vowel: The complete line reads: litora, multum ille et terris iactatus et alto. Scanned metrically, with elisions: litora, multillet terris iactatus et alto.)
The relevance to "h" is that a word beginning with "h" will not keep a vowel from being elided with another vowel. I'm not sure I can quickly find an example in Aeneid 1, but I'll keep looking!
There's a (rare-ish) hiatus involving an "h," in Aen. 1. 16:
posthabita coluisse Samo: hic illius arma,
Normally, the -o at the end of Samo would be lost (elided) in front of the vowel "i" in "hic," but, for effect, the elision doesn't happen and we have a hiatus instead.
OK, in Aen. 1. 65: Aeole, namque tibi divum pater atque hominum rex
which is read, with the elision of the -e of atque before the -o of hominum (so the h of hominum doesn't 'block' it): Aeole, namque tibi divum pater atquominum rex.
We can also point out that the "h" doesn't "count" as a second consonant in making a preceding vowel long: at the end of Aen. 1. 63, for example, we have iussus habenas, with the metrical pattern LONG short short LONG LONG; in other words, the final -s of iussus , though followed by the initial h- of habenas, does not cause the -us of iussus to be scanned long.
That's quite technical, but it's the best I can do, to shed some light on the question.
When habere ("to have") governs a reflexive object pronoun and is used with an adverb, it means "to be (in a good or bad way)", depending on the adverb chosen.
Tu te habes: "you are feeling..." , "you are in (some state)": we're waiting for the adverb, like male "bad" or bene , "good."
The question-word is the adverb quomodo, "how?" , "in what way?", so the one who asks the question is waiting to hear male or bene in the answer.
Me bene habeo, "I'm doing fine;" Livia se male habet, "Livia's not doing well / is in a bad way," and so on.
But Tu and Te don't mean the same thing, any more than Ego and Me mean the same thing.
They refer to the same person, yes; but Tu (and Ego) can only serve the subject function: You are fighting/You go to the store / You are happy. And Te (and Me) can only serve the object function: I scold you / I take you with me / I send letters to you.