Simple past tense expresses an action that happened in the past and has finished. So your examples:
I find/found you pretty cute.
You can use either "find" or "found", but the meaning changes somewhat. If you use "found", as by the definition of simple past, it implies it is something you once did and no longer do. Therefore "I found you pretty cute" implies that you no longer think so. It makes for a fairly effective veiled insult. You probably mean to say "I find you pretty cute."
Thank you, I understand/understood it.
You can use either interchangeably, though again the meaning changes somewhat. I understand means in this moment you understand, which might imply that you've just now understood something. In other words: thank you, I didn't understand it before, but now I understand it.
Due to the nature of understanding that you can never really stop understanding something, by using "understood" you imply that it is something you knew prior to the explanation. In other words: "thank you anyway, but I had already understood it."
I'll call you after I arrive/arrived there.
If you break this sentence down, there is only one grammatically correct sentence, and that is "I'll call you after I arrive."
This is because you cannot use the past to describe something that hasn't happened yet. The present tense can be used if it describes an action that will happen in the near future. If it is in the distant future, it is better to use the following:
"I'll call you after I'll have arrived."
This case is called future perfect and it implies an action that will be performed in the future. You don't hear this tense used too often though.
For the most part these are subtleties. For your first two examples, present would probably fit everyday usage 90% of the time, so I would suggest you to use present when you have doubts. Only if you specifically meant to say that an action was performed in the past and has finished, should you use simple past as a general rule.