Windows 8.1

Normally setting "public network" is for connection by WIFI to a public hotspot.

but

If I use it also to connect my portable at home to my internet provider by WIFI (there is no other device connected to my PC other than a wireless mouse, no other device connected to to the WIFI neither). No home network , just my PC.

The speed of the connection will be faster than if I use the "home network setting?

Could I have problems to get automatic microsoft updates?

any other advange or disadvantage for using the setting "public network" also at home?

Many thanks

  No, it will not make any difference to the speed. It is a security setting.

As a general rule, public is of no use on a home network because it prevents file sharing between devices.

No difference its just privacy settings your computer is trying to hide itself in this setting and may log out of sites quicker which isnt convenient at home but is a good idea when out and about.