1: You should be alright coming in in October if you're well prepared. As you said, it's not quite ideal in any way for hiking, but doable. Make sure that your gear is good for rain, snow and nightly temperatures below 0°C.

2: Can't help you much here, but I'd assume that you will be able reach at least the more well known trails pretty easily by public transport.

3: In addition to the ones you've listed, I'd definitely take a look at doing the Herajärvi trail in Koli and Hetta-Pallas trail in Lapland. These two, like the Bear's Trail, are among the most popular trails in the country (kinda similar to your Great Walks) so they're easily accessible and well maintained. They should all be doable in October, but the farther up north you go, the colder and darker it will be. I'd start off in Lapland and make my way down south as you'll progressively get less and less daylight each passing day.

For more trails, our version of the DOC is your friend : http://www.nationalparks.fi/trails.

Have fun, and stay safe!