As a girl, if I didn't personally make sure someone had my contact information, and I left the site they'd met me on, I would be rather pissed off if they tracked me down on another site.
Point blank, I doubt she's interested in you. If she was, she'd have personally reached out to you. Don't overstep boundaries.

Yes it's weird. Stalker-ish, even. Proceed with extreme caution...if you so dare.

No. Go for it. But you must have an excuse. Linked in seems to be a professional site so if you're in a profession too, preferably one similar to hers, the excuse could be easy.
Otherwise, it's harder.
If you just found her linked in account at random and if you're not there and if you absolutely know you're interested in her but chances to meet her are negligible, then go for it again, but apply a direct strategy: "I stretched for you everywhere, I'm mad about you..." That kind of thing.

In any case, go for it is my advice, but apply a different strategy depending on your situation. Remember that there's a sure way not to get her: by never telling her.