For centuries before Jesus' time, there have been 23 prophecies that were said to pertain to the Davidic Messiah. Mark listed them. No others were ever recognized by Jews before, Christianity back-engineered most of the so-called 300.

As far as the Nazareth thing, it all comes down to a quote in Matthew 2:23
And he came and dwelt in a city called Nazareth: that it might be fulfilled which was spoken by the prophets, He shall be called a Nazarene.

The problem is that there was never any prophecy stating anything about Nazareth or a Nazarene. You can search in any version of any Old Testament and you cannot find those words - relating to the Moschiach or otherwise.

I have seen it referenced back to Isaiah 11:1
1 And there shall come forth a shoot out of the stock of Jesse, and a twig shall grow forth out of his roots.

but I have never understood how they got a Nazarene out of that.

The other interesting thing is that Nazareth didn't exist in any references, anywhere except the Bible, until about the 4th century CE.