Translation:Please take a look at this agreement.
Please have a look at this contract should be accepted. Agreement and contract can be used synonymously.
Not really, only contracts are legally binding.
However, in a non-legal context, 协议 can mean both a contract, which is legally binding, and an agreement, which may or may not be. In light of that, while it seems duolingo means "agreement", both should be acceptable.
It makes the request "softer". It implies a sense of taking one's time, or just doing something for a little bit. In other words, it makes the less harsh and less abrupt.
Duo has tried to capture this feeling on English with "take a look" instead of just "look".
协议和合同是一样的吗?Are the two words "xieyi" and "hetong" the same/interchangable?
Good question, I did a small search and found the following:
In essence they mean the same thing but the law states that 合同 is a 协议 entered into by parties of equal bargaining powers, so there's a subtle, if legally non-existent, difference there. However, in a non-legal context, 协议 can mean both a contract, which is legally binding, and an agreement, which may or may not be. In light of that, while it seems duolingo means "agreement", both should be acceptable.
'qì yuē' is a more formal term for "contract" or "agreement", one could even call it business and legal jargon. As in English, it covers the many areas where an agreement or a contract is used between parties through speech, actions, or in writing.
Source: 百度百科, sort of the Chinese version of Wikipedia. https://baike.baidu.com/item/契约/2874688
For a more comprehensive and rather too detailed for duolingo understanding, check out https://wiki.mbalib.com/wiki/契约. It basically says that 契约 is equivalent to the concept of a "contract" in English, which in normal usage may or may not be legally binding, in part or in whole.