Hi Erik,

أنا ذاهب إلى المدرسة, reflects the meaning you seek. Note that the verb 'ذهب' is written with thaal (ذال) instead of daal (دال).

أنا ذهبت إلى المدرسة, would translate into: I went to school. Also note that in this sentence, the verb 'ذهبت', by using the special pronoun (تاء المتكلم), already makes it clear that the sentence is spoken in first person. So the word 'أنا' becomes somewhat redundant. 'ذهبت إلى المدرسة' is more natural-sounding.

Be well!

Hi Erik,

My answer turned out to be huge. I will break to smaller portions to bypass italki's character limit

Arabic has a special property called "'i'raab" (إعراب), wherein an extra vowel is added to the last letter of a given word depending on its position and role in the sentence. This property is responsible for the 'u' and 'un' sounds you observed in the above sentences.

'I'raab adds an immense layer of complexity to Classical Arabic. Depending on the complexity of the grammatical structures utilised in the sentence, identifying the correct vowel at the end of each word can become a game of cat and mouse, but through enough exposure and hard work it can become second nature. I recommend that you stick to learning Arabic without taking I'iraab into account; only think of I'iraab if you are seeking thorough mastery over Arabic language.

Do not let any of this confuse you. I'iraab is a concern if you are intending on reading Qur'an or heavy literature texts, deliviring newscasts and public speeches, or sensing the 'musical' flow in classical poetry. With the over-reliance that native speakers have on their spoken dialects nowadays as opposed to fus-ha Arabic, few people show geniune interest in mastering these advanced aspects of the language.

I hope this answers your question.

Yes, they are one and the same as far as beginner MSA is concerned.

you should say

انا ذاهب الى المدرسة