How many licences does Windows 7 Ultimate come with?

This should be answered by Microsoft. Usually the user agreement will have this info.
You get one computer activated per key regardless of version.
The Ultimate version has features that are unnecessary for most consumers, and most are perfectly fine this round with Home Premium, or perhaps Professional.

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It's very unlikely you need things in Ultimate like BitLocker or the ability to use lanugage packs. Ultimate is feature-wise the same thing as the high end Enterprise business edition, but just a way for consumers to get the extra features if they desperately want them.
Microsoft is supposedly going to have family packs eventually available where you'd get 3 Home Premium activations (i.e., use for 3 computers) likely somewhere in the $150 ballpark.

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Step one would be to confirm that you really really truly want and need the couple pricey extra features in Ultimate -- you almost certainly don't. They're mainly useful for some business environments where there might, for example, be a laptop shared by multiple people speaking multiple languages and regularly traveling internationally where the BitLocker security would be useful as well.
One licence per installed Computer is required. So sharing with several computers is not allowed, but using the copy with several users on one machine is no problem at all. But I don't think that's what you had in mind.

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generally speaking, unless stated otherwise, you get one license per key
I have a gateway 818GM desktop computer but when I use the windows disk to install a fresh copy it says "some hardware did not install correctly due to invalid data." This is during setup and it finishes through setup and installs windows but of course windows does not load. It just keeps restarting. The reason why I am installing windows again was becuase this issue while windows was working and I could not install a wireless card due to it. Any help would be great, Thanks.