The easiest way to solve problem #1 would be to create a 6th VLAN with its own subnet and give the ASA inside interface an address on that subnet. Make that address the default route for your L3 switch. Other options would be to run a routing protocol (EIGRP or OSPF) between the ASA and L3 switch or make the interface a trunk and use subinterfaces on the ASA.
I don't know anything about ADSL bridge mode so I can't help you much with that one. Generally speaking, an ASA can only have one default gateway though and it cannot do policy-based routing. For that, we typically use an actual router which gives us many more options in influencing the path traffic takes.