In case you are curious what the exact reason might be:

"It seems to me" is most likely coming from the much less fancy sounding, and more casual "мне кажется" (mnye kazhetsya).

"Mnye" would be "to me", and "kazhetsya" could be represented as "it seems". I say "could be" because there is no direct translation for "kazhetsya" as far as I'm aware.

The closest (and most direct) translation of "kazhetsya" that I can think of, and retains the meaning would be "it seems likely that <...>".

What she was trying to communicate was "I think", I think. (pun intended)

Like "Me parece" in Spanish.

Coming from English, I struggle with when to use я vs Мне.

Not sure if you'd like an advice or merely sharing your experience, but after reading your comment I spent an hour or so trying to provide a simple rule of thumb. To my surprise, I failed miserably. But I scraped some info together in the process, so I'll post it in a hope that it might give you a better perspective. Mind you, I'm not a linguist or a teacher.

First of all, I made a list of Russian я/мне lines with English translations next to them just to see if there is consistent presence of a hint in English lines that can point to the right Russian translation. There is none. So if you are trying to figure out the proper pronoun this way, you are doing it wrong.

To make an educated choice between я/мне you'll have to familiarise yourself with nominative and dative cases.

Here is some basic info on the cases in "question" and even more basic examples:

Nominative case of "I" is "я". Nominative case answers questions such as "who?" or "what?".

Кто пришёл? (Who came?) Я пришёл. (I came.)

Dative case of "I" is "мне". Dative case answers questions such as "to whom?" or "to what?".

Дать кому? (Give to whom?) Мне. (To me.)

As you might've noticed, native English speakers won't normally construct questions in a way they are constructed in most Russian cases, so I'd suggest to get familiar with cases and their respective questions first, and try to construct sentences later.

Or, depending on your goal, you can simply memorize common sentences/lines altogether and figure out why they work later.

Thank you for taking the time to write this. And good point regarding dative case. I should just think in terms of sender/receiver.

Where I especially get mixed up with Russian is when dative and acusitive are in the same sentence. Next up for me is instrumental case - oh boy

I had an Austrian friend that learned all his English from star trek TNG and DS9... it was amazing :D

He'd watched the series in German and then in English and knew it well enough to pick things up.

To my ear, his English was pretty good.

That said, the 2 groups of non-native speakers that have impressed me the most are people from Sweden and Norway. I've mistaken more than one of them for native speakers (to their delight) :D

I desperately want to do this in the other direction, but I can't figure out how to stream foreign dubbed trek in the states and I don't have a DVD player anymore... It may take a bit more effort.