"te quiero que lo hagas" is
agramatical because "te quiero" means "I love you" and there's not even the possibility of it meaning "I'd love ..." (me encantaría).
Quiero que lo hagas ---> I want you to do it.
Quiero que tú lo hagas ---> I want YOU to do it / I want you to do it (and not someone else)
but
Te ordeno que lo hagas ---> I command you to do it
Te ordeno que te calles ---> I command your silence
Te ordeno que me prestes tu total atención ---> I command you full attention.
These are more along the lines of what you're asking in the OP.
From command to supplication, any exhort seems to need the by-whom to-whom parts to be clearly marked off. That means a "yes" answer to your question #1 ... but not totally. I would expect everybody to understand what I'm saying about Spanish indicative not being English indicative and Spanish subjunctive not being a capricious way to express certain instances English indicative and else, with "que" being magic word that points something is being "triggered" some place else by who knows what.
To feel how this exhort thing works, a fragment of a song that was a hit when I was eagerly waiting for the time to come when that glorious part of life called teen age would be part of my life (so, prepare to fly 43 years into the past), and everyone knew how to play it in their guitars or at least, to sing the lyrics. It's a tragic rock ballad of a lover who is trying to get being reached by his/her recently lost half through the grave.
It's lyrics are a great practice for the grammar bit you're asking about (if you forbid the horrible spelling mistakes of the person hanging the video).
About question #2, I think you are doing what everyone does regarding a foreign language: trying to use the model of you native tongue when there's no clear information available to you. If a problem, it's everyone's, including me, and not solely yours.
Just compare your two languages, the native one to the one you're acquiring: English is extremely dependent on word order ... "boy band" is a band made of boys, and "band boy" y a boy who plays of sings in a band. Made that into "chico banda" and "banda chico" and you get the king of gibberish one only hears as mock Spanish in the recording of a techno-salsa American style. In that short scale, Spanish is dependent on coordination and articulation "buena banda" and "banda buena" -not exactly the same- or "buenas bandas" and "bandas buenas", but don't dare to say "bandas buena" because we'd fall in gibberish territory instantly.
When we take another step away, new structures start to show:
Quiero que vengas ... que vengas quiero
I want you to come ...
to come I want you
The notion conveyed in both languages contains two verbs that are in risk of clashing and render the phrases unintelligible (Quiero que vienes* I want you come*) One verb is clearly an action and the other verb is treated as a thing or notion. The trick of English: made it into an infinitive ("to come"). The trick of Spanish: forbid this to be done by indicative and create a whole new mood to deal with these "actions behind a muffler". Spanish invented a whole new conjunction just meaning "hey, here it comes!" stylized as "que", and that brings certain freedom to order your building blocks the way you like.
To make things short(er), when you see a clause introduced by "que" try to get involved deeper in the way Spanish works. Don't try to make it into "yet another instance with magical triggers that one should be aware of" or "another irritating situation that should be dealt as vocabulary" (I'm not saying that you do that, but every English native learning their SSL do it in some degree).