I have an opportunity to exchange links with another site owner but I would like to check to make sure the link he leaves me will pass link juice. Is there a way to check for robots.txt?
Just download robots.txt and you will see if it's prohibited.
Yes, you can check if the link is nofollow or dofollow because Dofollow pass the link juice.
For checking robots.txt, you can use tool or use /robots.txt after the domain name.
You will use NoIndex when instructing a search engine not to store your web page for display in search results while you will use NoFollow when you are instructing search engine crawlers not to follow the links that are on your page.