I am trying to figure out if an L3 switch is able to act as a switch for himself.
That's a main point of an L3 switch. It switches on L2 and routes between VLANs.
Is it possible to configure somehow the L3 Switch to act as a switch so that I can set up VRRP?
Provided the L3 switch supports VRRP then yes, that's possible. For full functionality you need to set up an SVI on a VLAN and not use a routed port (since a routed port doesn't support switching in case of failover).
Note that VRRP provides gateway redundancy for end nodes. Routers simply route across common subnets. With more than two network you'd need to provide routes to remote subnets though, using static routes or by setting up a routing protocol like OSPF.
It's easiest to visualize an L3 switch as an L2 switch with an integrated but seperate router. While the switch forwards frames between switched ports and SVIs (but only within a VLAN), the router forwards packets between SVIs across VLANs) and routed ports.