Are there sentences where 跟 and 和 are interchangeable?
Both of them are correct, and the 跟 &amp; 和 here are the conjunction. The one 我同朋友去公园了 is also correct.

They are almost the same, but if you do want to distinguish the meanings (except for the spoken/written difference):


我跟朋友去公园了。: it seems like my friend (朋友) wanted to go to the park (公园), and s/he asked me whether I wanted to go with her/him. So I just went with her/him and left a message to my mother: "Mam, 我跟朋友去公园了".
我和朋友去公园了。: it seems like my friend and I were doing something together (e.g. having lunch), after it, we decided go to the park together.


Maybe that's not a very good example. But I cannot think of a better one because both of them are almost the same (99.9%). :p