I suspect that you are saving LARGE images. Check. It takes time to get these into your camera memory. SIZE is issue #1. Second, you might be using a "slow" memory chip. Today's large images encourage the use of fast chips, with upload speeds of 60mb/s or higher. I have most images from this camera at ~7MB/image. I use chips with speeds of 60mb/sec. SPEED is issue #2. You can set the JPEG compression to a higher compression, smaller saved image, and you can use faster chips.
The camera performance will improve if you do those. Check out the recommendations on the $2000 DSLR and they sortof explain this.

Slow auto focus is a real nuisance. If you are shooting action, like my hobby of shooting dancers, and it's in a club or poorly lit situation, the auto focus is a shot killing enemy, with virtually all cameras. The trick to minimizing the issue is to adjust the effective ISO, or "electronic film speed" to a significantly larger number, so that the camera can focus more quickly because the depth of field increases. But this increases "granularity" in the shot, with images likely to appear grainy our coarse. And with some cameras even that isn't good enough. I own some of these. Great outside, not good for moving subjects indoors where flash will be involved. Won't name names but it is an issue.

PictBridge is the name of an industry standard for firmware (built-in software) that allows digital cameras and printers to communicate directly with each other. The firmware allows a digital camera to send images to the printer without requiring the assistance of a computer or any special image-editing software.

A PictBridge-compliant camera connects directly to a PictBridge-compliant printer with a standard USB cable. Once the devices have established a connection, the camera will “talk” to the printer and ask which PictBridge functions the printer has. When the printer answers, the camera will display a menu on its LCD screen or viewfinder with print options. After a print function has been selected and the print job is completed, the printer will send confirmation back to the camera.

PictBridge is vendor-neutral but both the camera and the printer must be PictBridge-compliant for the software to work. The standard is overseen by the Camera & Imaging Products Association (CIPA). To determine whether a camera or printer is PictBridge-compliant, look for the PictBridge logo or consult the product specifications listed in the owner's manual.

In order for the background to be blurred you have to shoot with the lens "wide open" which lessens the effective depth of field. I am not sure what you mean by your comment on zooming in, but if you select the aperture as wide open and set the focus on the object you want to be sharp the camera will give you a shallow depth of field shot.