These are all great questions.
1. You should definitely provide a disclaimer and nofollow if you are providing products for free to the blogger. This is generally a requirement for compliance in the US and with Google's Webmaster Guidelines respectively.
2. The no-follow link isn't going to give you any real SEO value, but it could certainly give you valuable traffic if you are doing blogger outreach to the correct audience. To make blogger outreach valuable, you should be looking at your prospects for more than just a link. A good enough blog post could itself rank for valuable keywords!
Finally, you ask the question "is blogger outreach dead". It certainly is not, but there is more to it that just getting sponsored posts up. You need strong pitches that actually provide value to the audience of the blog you are doing outreach to. That being said, I find blogger outreach to be difficult, time-consuming, and and low ROI. Chances are, there are some more scalable link building opportunities out there.
- You could mine your competitors backlinks - for example, you should have a link on this page too.
- You could do a piece on fire safety, especially related to wood fireplaces, and resource page link building.
- You could try building an audience by sponsoring lumberjack competitions
There are a tons of opportunities which might be easier pickings, at least at the beginning.