Can I connect my Android device to a laptop via WiFi to use file sharing? How can I connect my Sony Xperia U to my laptop using WiFi to use file sharing?
I tried normal connectivity by sharing my laptop WiFi and connect my Xperia U to the laptop -- but it only accesses the internet, not the file sharing.

What should I do to access file sharing and managing my laptop using my phone? Is there any application, setting, or procedure that can help me connect my laptop and my phone?
Plenty of solutions available here. Depending on which device you want to work (i.e. using your Android device to push things to/pull things from your laptop, or working on your laptop and accessing the Android device), your choices may differ, though:

ES File Explorer is a file manager app for Android which also can access remote resources via WiFi. Amongst others, it supports CIFS (aka "Windows Shares") and FTP.


ES File Explorer (Source: Google Play)

AirDroid is an app running on Android, and offering access via web browser. So you can work from your laptop and access your Android device via a web interface.


Airdroid (source: Google Play)

Both variants require your Android device and your laptop being in the same network (well, there are ways around this restriction — but this is how it definitly works). Using the same WiFi access point for both should guarantee that, for example.