The english adjective "present" can be translated into German in more ways that those you mentioned:
The barbaric practice continues to the present day.
Die barbarische Gepflogenheit dauert bis in die Gegenwart an.
The translation of »present day« is just »Gegenwart«, so an equivalent of the word »present« doesn't even exist in the German translation.
Another example:
The present manager has a bigger office than the last one.
Der gegenwärtige Manager hat ein größeres Büro als der vorherige.
Der aktuelle Manager hat ein größeres Büro als der vorherige.
In this sentence »present« can be translated into »gegenwärtig« as well as »aktuell«. Both words was not on your list.
One more example:
Sorry, I was distracted just now, I'll try to be more present from now on.
Entschuldigung, ich war gerade abgelenkt, ab jetzt werde ich aufmerksamer sein.
Also »aufmerksam« was not on your list.
But now for the words you asked for:
anwesend
Is the witness present here in the court?
Ist der Zeuge hier im Gerichtssaal anwesend?
This means to be physically located at a certain place, and often also at a certain time.
The present visitors was overwhelmed by the artists performance.
Die anwesenden Besucher waren von der Darbietung des Künstlers überwältigt.
da
Note, that »da« is not an adjective. There is an adverb »da« and a conjunction »da«. Since the German conjunction »da« never can correspond to the English adjective »present«, I will not talk about the conjunction here. I just give an example: »Da ich nicht dort war, weis ich nicht was dort wirklich los war.«
The adverb comes in three different flavors:
local: Wann werden wir da sein? (only in German German, not in Austrian German)
temporal: Schließlich war der Augenblick da, den sie so ersehnt hatten.
modal: Ich kann dir da nicht zustimmen.
(A note to the first sentence: In Austrian German it strictly has to be »Wann werden wir dort sein?«, because »da« means in Austrian German: »The place where the speaker is.« In German German »da« also can mean a place far away from the speaker, while this has to be »dort« in Austrian German.)
Only the local version has a chance to correspond with the English word »present«. But since »da« is an adverb, and »present« is an adjective, I don't think that there are much English sentences, where »present« should be translated as »da«. I thought about examples, but I couldn't find some.
präsent
This is easy again:
As you already might have thought, the English adjective »present« and the German adjective »präsent« are the same word. They mean the same in both languages. Both versions of this word derive from the latin »praesens« which is present participle of the verb »praeesse« which means »to be before something«.
But in German it is not so often used as in English. In German »präsent« can by used as synonym for »anwesend«, but it always comes with a connotation of being dominant:
Der Heine-Verlag war bei der letzten Buchmesse sehr präsent.
This means, that the publishing company Heine was present at the last book fair in a dominant manner.
