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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.
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question
particle-に word-usage possession
How do i use ある/いる?
_[Edited to clarify answer]_

は is the topic marker so you have been using it correctly.

If you use には、you are emphasizing what is the case for the particular subject
of this sentence, but this might not apply to others. It implies a contrasting
element by 'pointing' at the subject. Like saying " **I** have wings (but
other people don't)". It stresses the fact that it is I who has wings. Without
the に、it's a simple statement describing that fact without any other
implications.

私はパソコンがある。I have a computer. (simple statement of fact)  
私にはパソコンがある。 **I** have a computer. (statement of fact+implying this isn't the
case for someone else)
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answer