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sorry in advance if devastating this nice poem. my try:

Sev beni, hala sev

Hep sev, yapacağını söyle

Özgürce sev

Öldüremeyecek kadar,

Şimdikimden bile fazla sev

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Poetry can´t always be translated and keep the same feeling.

Most of the translation seems fine, except in my opinion the line

Love me so without would kill

(love me so much that I would die if this love ever stopped)

Öldüremeyecek kadar (sev) doesn´t seem right to me in a purely literal sense, but maybe in Turkish it comes across differently

(love as much as it will not be able to kill)

anyway, at least you have one attempt to start with 

I would start translating it but then i bumped on this sentence that my little brain is not able to understand

"Love me so without would kill"

Beni öylesine sev ki aksi öldürsün

Beni öylesine sev ki sevmemen öldürsün

Aksi öldürecek kadar sev

Maybe something like these above.

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yes I think we can say all of these above, this one is clearer "beni öylesine sev ki sevmemen öldürsün", but what is this poem, did you write it?

"Sev beni, yine sev,

Daima sev, seveceğini söyle

Özgür iradenle sev

Öylesine sev ki aksi öldürsün

Sonra beni daha da sev"

something like this.

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