cum Phillippus Macedonum rex ab inimico necatus esset, regnum obtinuit Alexander filius eius, iuvenis tum vigniti annos natus. hic statim in pericula maxima venit: gentes enim a Phillippo victae sperabant se rebellione facta libertatem suam facile recuperaturas esse.Alexander autem tam celeriter in hostium terram profectus est ut nemo resistere posset et omnes sine proelia eum victorem salutarent.
When King Phillip of the Macedonians had been killed by the enemy, his son Alexander took over the kingdom, then a young man and 20 years old. Immediately this man came into great danger: the people by Phillip were themselves hoping for victories by rebellion, making it easy to get back their freedom. However Alexander quickly set out into enimy ground so that no-one was able to resiste and they would all great his victories without battle.
A very good translation. There a few very minor points that could be a bit smoother in the translation, but overall very good.
The only real error I see is a typo: “proelia” should be “proelio”.
Also I think there are some words missing in your last sentence, and note that they are not hailing his victories (victorias) but are hailing Alex as victor or conqueror (victorem).
When Phillip, king of the Macedonians, was killed by his opponent/enemy [in a personal sense] Alexander, his son, obtained government, a young man then twenty years old. He immediately came into great danger(s), for the tribes which had been conquered by Phillip were hoping that they, a rebellion having been created, would easily recover their freedom. Alexander however set out into the land of the enemy so quickly that no-one was able to resist him, and all hailed him as victor without battle.
“Cum ego verbo utar,” Humpty Dumpty dixit voce contempta, “indicat illud quod optem – nec plus nec minus.”
“Est tamen rogatio” dixit Alice, “an efficere verba tot res indicare possis.”
“Rogatio est, “Humpty Dumpty responsit, “quae fiat magister – id cunctum est.”