Do all links on a page have to be all underlined or all colored?

It is a standard that all text links follow an identifying convention. This can be your choice of any styling combinations, but generally speaking, they should all follow suit. An exception would be navigation elements.

1. Should all links be underlined?
2. Are all hyperlinks always the same Colour?
3. Should hyperlinks always be blue?
4. Why are some links blue and others not?

Should all links be underlined?

Assuming the link text is colored, it's not always absolutely necessary to underline it. There are two main cases in which you can safely eliminate underlines: navigation menus and other lists of links. However, this is true only when the page design clearly indicates the area's function.

Are all hyperlinks always the same Colour?

By default, a link will appear like this (in all browsers): An unvisited link is underlined and blue. A visited link is underlined and purple. An active link is underlined and red.

Should hyperlinks always be blue?

Some shade of blue is good, not necessary the default one. For desktop clients, adding underline on hover is nice and makes the color less important, but for mobile clients you need to convey that the link is clickable without any user interaction before.

Why are some links blue and others not?

You've no doubt noticed by now that while some links are gold and/or bold, most links out there are blue, especially on web pages of yore. But why? the TL;DR answer is that the Mosaic browser, released in early 1993 used blue links, and since the browser was widely distributed, blue just became the norm.