Do I have to route VCC and GND signals on PCB if planes are used
You would normally have a short trace at one end, long enough to get some soldermask over it, and then a via going through the board.  Placing the via directly under the end of the capacitor is called "via in pad".

The main disadvantage of doing that is that solder can disappear into it, leaving a bad joint. This isn't a huge issue hand soldering, but can be a big problem if you're going down the stencil/paste/reflow route, which you will when it comes to production. You can apply extra paste to compensate, use a small diameter via and/or only go through one layer of a multi-layer board to reduce the effect, or get the board house to plug and plate over to avoid it completely, but these options all cost money.

You might do this if you're really tight on space, to get better thermal management, or to get caps really clsoe to the IC at high frequencies. But usually, it's not worth the effort.

Depending on how you plan to solder the board, you might also want thermal relief at the other end of the cap, where it's soldered to the ground/vcc plane.