Up to now I've come to understand the meaning of these verbs. I understand when you are saying something exists somewhere you use the particle に to indicate where it exists, or someone having something.
In a recent question I asked about having something on your body, and now have come to understand you say something like: 「私には翼がある」(i have wings). After seeing this i feel how I've been using these verbs wrong when using them to mean 'have' in English.
To mark what would be the subject in an English sentence, would you have to use に?
「私にはお姉さんがいる。」
「私にはパソコンがある。」
I understand the implication of は and how it works with other particles. If it helps i'll make this a little more general. I've come to understand that は takes another part of the sentence and marks it as the 'topic' or 'scope' of the sentence. But something that has always confused me is when using phrases like: 数学が上手です、花があります and チョコレットが好きです。 Becase they mean: i am good at maths, there is a flower and i like chocolate. But when you are specifically introducing, who likes chocolate, who has the flower and who is good at maths because you are no longer the subject i've come to understand that in this case you use は and only は. I'm asking in the case of ある is it supposed to be に. becuase that intuitivelly makes sence for me:
「私に(は)鉛筆がある」
because it is basically saying there is a pencil, on me. or maybe can be stretched to mean in my possession.