Just blow out the joints and re-grout them properly.

You cannot pour concrete on top of pavers. It will be a broken mess before it is fully cured.

Its not hard to pull pavers out and the base should be good for your concrete pad. Put them on Craigslist for free if you don't want them and if you want some color to your concrete that can be added when they pour. A broom finish is a good gripping non shiny finish that might be what you are looking for.

The correct height is the patio must leave 2" exposed of the concrete foundation wall below the stucco, when the patio is touching the house wall. In fact, there should always be 2" to 6" of your concrete foundation exposed all the way around the house, so your aesthetic expectations should be adjusted to what is functionally required.

If the 4" step is awkward right at the door, you can raise a large landing there. Also, you cannot pour concrete over pavers, and pavers are considered a higher value and aesthetic look over concrete.

3 onthetree just beat me to it. Pull up a section of pavers underneath the door and create a higher landing pad if that's what you want. You don't need to pull out an entire patio to fix one area - that's one of the many benefits of using pavers instead of concrete.

Also, for the love of all that is holy, please don't pour concrete over pavers. I'd like to say any reputable contractor would refuse to do that....but after some of the things I've seen, I guess I should know better by now too.

Would caution against trying to raise the patio level any nearer your house finish floor. You could easily get water intrusion into the house if you raise the patio too high.