Re: How do I fill in the space...?
In the bathroom, it might be a good idea to seal the joint to prevent water intrusion into the structure in the event of an overflow.
I would recommend using a grout that matches the grout in your stonework. If the floor isn't grouted, use a grout that goes well with the stonework and the wood. If you use a caulk, choose a color that blends well.
I'm not a big fan of silicone caulk as the bond seems to fail after a few years, giving you an ugly crack between the caulk and one of the surfaces. Consider a polyurethane or butyl rubber caulk; acrylic latex tends to dry out and crack. (I'm not an expert on caulk; that's just my experience.) There are other, fairly new caulking products out there that I'm not familiar with which may do the job with great success. With grout, you will likely end up with a hairline crack against the wood, but maybe the crack will be small enough to prevent significant water intrusion.
If it's not too much work to remove the base trim (and won't damage it), you might want to caulk the floor/wall joint behind the trim before grouting between the floor and the trim.
As for the living room, it's purely an aesthetic choice.
The "Senior Member" designation under my name doesn't mean I know a lot, it just means I talk a lot.I've been a DIYer since I was 12 (thanks, Dad!). I have read several books on various home improvement topics. I do not have any current code books I can refer to. I was an apprentice plumber for two years.