Tagalog has a complex conjugation pattern for verbs based upon something called "focus". A verb changes its conjugation not just for past/present/future but also because of the word or idea you want to focus on. This is a concept that does not exist in English. As an example, consider the following four questions: Who bought the fish for us? What did Peter buy for us? What did Peter do for us? For whom did Peter buy the fish? Each of those questions can be answered in English with Peter bought the fish for us. But we would intone or stress the word(s) we want to focus on. PETER bought the fish for us. Peter bought the FISH for us. Peter BOUGHT the fish for us. Peter bought the fish for US. In Tagalog, they may still intone some words, but the verb bili (to buy) is conjugated differently based upon what the speaker want to emphasize. Si Peter bumili ng isda (focus on the subject) Si Peter binili ang isda ... (focus on the object). Si Peter ibinili ...(focus on the beneficiary). Therefore it is important to have a fundamental understanding of these different conjugation patterns. In the question you asked I see ikinagagalak and ikinalulugod. Since I know the i verb conjugation, I see kagagalak conjugated as an i verb in the past tense, so it turns into ikinagagalak. I see kalulugod conjugated as an i verb in the past tense also, so it turns into ikinalulugod. Each verb has a ka prefix, which adds another dimension to this I will not discuss at the moment. The important thing for now is to get to know verb roots (galak and lugod) and get a fundamental understanding of the different conjugation patterns based upon focus. It's difficult, but at least it will get you in the ballpark in trying to understand the meaning of verbs and to recognize them when they get conjugated.

I think the prefix "ikina-" tries to fix the focus of the sentence on the cause or the reason for the action done aka verb? "Ikinagagalak kong makita ka dito." (I am pleased/happy to see you here.) Galak is pleased/happy. You are pleased because you saw me (or whoever you were talking to) "here". It helps you focus on the reason for the verb.