If your status update is posted to only Friends, and no one is tagged in your post, then Joe's friends will not see the post or the Like on the post unless they are also your friends. This is (c) if there is no tagging or mutual friends.
If it is posted to Friends and Joe is tagged in the post, normally that will make the post and Like visible to Joe's friends as well. Joe's friends may see it in their News Feed, although they may not (Facebook determines what it thinks is most relevant for your News Feed, especially if you have a lot of friends). Joe's friends may be able to see the post on Joe's profile/timeline, although Joe may have removed it from there or may have changed this using his Privacy Settings.
If a post is not visible to someone then that person will not be able to see Likes on the post either.
Depending on your privacy settings, your newly added friend should be able to see your status updates yes.
Underneath every post in Facebook is a little icon, showing who can see that post. When you hover over it, it will tell you in more detail what the icon means. A globe means the post is Public (anyone can see it), 2 little persons mean only friends, the same 2 persons, but the right one in a lighter gray means friends except people who you added to the Acquaintances list, a padlock means only you, and a gear symbol means custom settings, which you can figure out by hovering over it. On your own posts, you can click this icon, and change it to whatever setting you want for that post. When adding a new post, you can also change it.
When a post has the privacy setting of Friends only, and you add somebody as a friend, they are now able to see that post. You could mark all your posts as Friends except Acquaintances, and add that person directly to your Acquaintances list, and they will not be able to see the post.
When you go to your own profile page, on the top right (just below your cover photo, next to the button Activity Log) is a gear icon. When you click that, and in the menu select View As, you can look at your own proflie through the eyes of somebody else. Like that you can see what that person could see on your profile.
Best Answer
One of my Facebook friends actually liked a page earlier today and posted a comment on one of the page's statuses.
When I went to my News Feed (set to "Most Recent"), it told me that my friend liked the page, but it didn't tell me that he posted a comment on one of their status updates. When I switched my News Feed to "Top Stories", it didn't tell me about his like or his comment. So depending on how your friends have their news feeds set up, they might see if you've liked a page, but they won't see if you've posted a comment on a page.
However, I also have my friend in the Close Friends list, and when I clicked on the Close Friends list, it told me about both of the things he did - that he liked the page and also that he posted a comment on the page. So if any of your friends have you in their Close Friends list, then they'll be able to see all your likes and comments when they click on the Close Friends list.