There are four tenses: contemplative (future), progressive (present), completed (past), and the infinitive.
As for conjugation, there are three main types of verbs: "mag-", "ma-", and "-um-". These affixes refer to their infinitive marker.
Infinitive: magdala (to bring)
Infinitive: matulog (to sleep)
Infinitive: kumain (to eat)
Past: kumain [*note how the infinitive and the past tense conjugate the same]
OR (if there is no initial consonant)
Infintive: umulan (to rain)
Is there a difference between "I learn" and "I am learning" (the first means for example "i learn tagalog", while the other is "i am learning tagalog at the moment i'm writing this")
As far as I know there is no difference between those two, ordinarily it is simply taken from inference or from context.
Adding personal pronouns after verbs is the only way to determinate who is affected by the verb?
Yes, almost always.
There are cases where none is needed - I forget the grammatical term, but it is during sentences such as "It is raining." Nothing can really "rain", but English requires the "it". Just as French requires the "il" in "Il pleut." In Tagalog, however, you can simply say "Umuulan."