The general rule with Holy books is that we don’t take them into bathrooms/toilets, should be covered in a bedroom and so on. The question ise is if this would apply to Holy books in electronic format. On my iPaq, I have copies of Shulchan Aruch, the entire Tamud Bavli as well as the Siddur and Tehillim, plus a few extra other books. Since the iPaq is also my phone/diary and so on- it generally goes where I go. So is it a problem to have the books on it, or is it ok as long as I do not open them in inappropriate places?

It is ok as long as you do not open them in inappropriate places.