I installed new photoshop, and working on iPhone and Android apps looks nice (for android at least on xhdpi and hdpi, mdpi and ldpi require zooming in) but when working on website layout i get frustrated to zoom in to 200% in order to see the page as it is online and see text all pixelated. Is there an way to render shapes and text as vector, to keep it sharp regardless of zoom level?
Unless you are intentionally rasterizing text, it is vector.
Your screen displays content in pixels though. Your monitor, or any monitor, can't display vector output. They must use pixels for output. Photoshop uses a pixel preview and remains true to pixels when zooming so as to allow editing on a per-pixel basis when zooming.
A monitor with a higher pixel density would improve the appearance when zoomed slightly. Beyond that, there's little you can do.
It maybe helpful for you to open two windows of your current document. This will allow you to view what you are working on at multiple zoom levels while you work. I often do this so I can edit pixels zoomed in and see the overal effect of edit from a more standard zoom level. Simply choose Window > Arrange > New Window for [document title].