Almost. They belong to two groups (reason and purpose) with their respective question words.
- Synonyms of Why - Because/That is why, Asking for and giving a reason.
Warum? Darum. Weshalb? Deshalb. Wieso? (Daher) Weswegen? Deswegen.
'2. Synonyms of for what? (Wherefore?) - for that. Asking for and giving a purpose.
Wozu? Dazu. Wofür? Dafür.
deshalb, darum, deswegen are synonymous. they are pointing out a reason. "Uns fehlt Mehl. Deswegen können wir keinen Kuchen backen." (we do not have flour. Because of that we cant bake a cake.)
dazu is used in sentences like "dazu nimmt man Mehl" (to do this use flour) or "Gib mehr Mehl dazu" (add more flour). None of the d-words would work here.
für das... hard to say without context. Definitely does not work in this sentence. You sure you dont mean just "für" and das ist an article like "Für das Auto brauchen wir mehr Stahl."
We are not looking. translates to
Wir sehen nicht hin.
Usually, sehen only translates to to see. The translations for to look are mostly the variants of -sehen with a prefix (aussehen, hinsehen, vorsehen, übersehen, besehen,...). If it is a separable prefix, it can be hard to spot, that it is actually a different verb than the plain sehen, because a separable prefix can move to the end of the sentence.
Ich sehe gut. (sehen wihout a prefix) I (can) see well.
Ich sehe gut aus. (aussehen) I look good.
Ich sehe hin. (hinsehen) I look (there).
Ich sehe mich vor. (vorsehen) I watch out (for myself)
Ich übersehe es. (inseparable prefix) I overlook it.
Ich besehe es. (inseparable prefix) I look at it (from all sides)/inspect it.
Wow... Thanks for all of the cool examples (and not just throwing out a link). I have a better understanding of the fact that it can mean many other things. I SERIOUSLY DOUBT that Duolingo could have have taught me that. I'm glad you and other speakers are here. This is still a very difficult road but I'm trying. The plan is to complete this tree and then get some 4-6th grade books and start over.
This should help: https://forum.wordreference.com/threads/deswegen-vs-deshalb.2805551/#post-14177185 (it's in German, if you don't understand something, do say)
You are on the right track, but "halb/half" did not only mean divided by two but also side and direction. So think of "deshalb" as coming/resulting from that direction/side, which is indeed similar to "deswegen" "from that way" and "daher" (therefore/"therefrom").
An English word with this sense of "half" in it is:
"behalf" from "by + half"
This went into the direction "towards an intrest" (side) and there are even similarities with
"because" from "by + cause"
Other German words with the "halb/half" stem are those that end in -halber and "halber" itself, which again means because/caused this way.
interessehalber (adverb) - aus Neugier/out of couriosity · da es auch andere interessiert/since others may be interested · wegen des bestehenden Interesses/because of current interest
Here are some links to browse etymolgy and usage.