The reason America joined WW1 was because they intercepted a message from Germany to Mexico asking them to invade America. If Mexico received this, what was the likelihood of them invading, and if they did, how much of a problem would it have been for America?

Alright - first of all "what if" questions are always difficult. Fortunately, we know the Mexican response to the Telegram, and that was to remain neutral. The United States may have intercepted the message, but the Mexican government still received it.

Second, the United States didn't really join the Great War because of the Zimmerman Telegram. Though one could argue it was a contributing factor. Anticipation of United States entry to the War was the impetus for the message.

Zimmerman sent his Telegram several days after Germany decided to resume unrestricted submarine warfare - the policy of sinking any ship entering British waters. It was the German government's assumption that this (submarine warfare) would lead to the US declaring war.

A U-Boat sunk an American ship, the Housatonic, in February of 1917. This prompted Wilson and Congress to act. . The United States began preparing for war in the same month. On February 22, Congress passed the Arms Appropriation Act. Germany continued to sink American ships.

As for the Zimmerman Telegram, Mexico did receive it. The Government investigated entry into the war. However, it wasn't plausible for them to act on the invitation. Mexico was involved in a Civil War - that and several other factors contributed to their neutrality. Even so, Mexican involvement was a concern. In mid-1917, the United States formally recognized the Carranza (the Mexican President) Government to further ensure neutrality.

This is a fairly straightforward question, and I answered this off the top of my head. I am happy to provide some sources for further reading upon request, though.