Q. I'm doing a 5x5. Do I need to do a valsalva for every rep and/or hold my breath for every rep?

No and no. There is no need to by worrying about a valsalva for the intensities encountered during a typical 5x5 and there is really no need to ever hold your breath. When you combine the volume and the relative intensity of a 5x5 you will get into much more trouble holding your breath than you would with just a maximal lift or very low reps.

When we encounter problems with blood pressure changes that are one thing that can lead to exertional headaches, dizzyness and that kind of thing, it is usually volume related. Going up and down too fast and big changes in pressure do to the heavy lifting combines with a lack of time for normalization between reps. Holding your breath or attempting to do valsalva for every rep without a lot of control is not a good idea and really unnecessary.

2. Should I be breathing into my belly?

This is a trickier question. First of all "belly breathing" is really incorrect and a misunderstanding of the full picture. That is, the message that all the breath should be "taken into the belly" which results in an unnatural distension of the belly is incorrect.

People have misunderstood the problems with high chest breathing to mean that you should not be using you ribcage at all and instead should concentrate all breath to the belly. They think this is "diphragmatic" breathing.

Instead, correct breathing starts with the diaprhagm and then continues into the chest cavity..which I will explain in more depth in other articles. This kind of correct breathing does not result in the shoulder rising in excess. Indeed trying to artifically focus all breath into the belly could cause problems as well as there are a great many secondary muscles which contribute to breathing.

See Parodoxical and Diaphragmatic Breathing for further reading.