There are already a ton of threads on the subject. Have you searched for them? Yes you can have a wood counter and a stainless steel sink. Having wood will involve more maintenance, but not necessarily all that much more. It will depend a lot upon how you and your family use the kitchen.

I have a maple, wood plank island with a farmhouse sink. I just wipe it down after I use it, which is a little more work than I used to have to do to my solid surface countertop. But, it's worth the extra effort, I love the look of the wood! It's sealed with a butcher block sealer and so far I've had no issues.

Yes, you should be concerned over the long term. Water will take its toll over time, not just on the wood, but on the glue that holds bb together. If you are considering this you might want to use marine varnish around the faucet cut outs especially.

I can't post images right now, but one of my faves is of a maple butcher block island with a soapstone sink AND sink surround. How would you feel about having a bit of stainless surrounding your stainless farmhouse sink, about a foot on each side, then transitioning into bb? That surround will save you from a ton of maintenance and decay over time.