「I’m a third year and my friend is also a third year. Would I address them as Senpai or -san?」
Out of those two, you'd use -san. If both you and your friend are third-year students, neither one of you would call the other senpai, regardless of when your exact birthdays are, because "senpai" doesn't mean "older person."
The 先 part of senpai/先輩 means "before," so it's used to address someone who became a member of a group before you. For example, if Taro is a first-year high school student at a school and Jiro is a third-year student, Taro could call Jiro senpai, because Jiro became a member of the school two years earlier than Taro did.
But if you and your friend are both third-year students, then you became members of the school at the same time, and so neither one of you is senpai to the other.
Plus, in purely practical terms, if people in Japan had to call their classmates "senpai" just because they were born earlier in the school year, it'd mean that you'd have to remember when all of your classmates' individual birthdays are, which is way too much of a hassle for anyone to be OK with.
「And does the Senpai/kouhai apply in sport teams? For example addressing the team captain as Senpai even though you’re in the same year?」
Yes, members of sports teams call their upperclassman teammates senpai. However, the captain doesn't get called "senpai" unless the person talking to him is from a younger year.
For example, if Taro is a first-year student on the soccer team, and Jiro is a third-year student and the team captain, then yes, Tao could call Jiro senpai. However, if Saburo is also a third-year student on the soccer team, he wouldn't call Jiro senpai, because thy're both in the same year.
To summarize, even though "senpai" often gets translated as "senior," it's not used exactly the same way as that word is in English. It doesn't mean that someone is older or higher-ranking than you, just that they've been a member of something longer than you have. However, since the word senpai is most commonly used in schools and companies, generally your senpai is going to be someone older than you (switching companies mid-career isn't as common in Japan as it is in many other countries), and with a lot of promotions in Japan being seniority-based, usually your senpai will be higher ranking than you too, or at least the people higher ranking than you will usually be your senpai.