You also ask about VPC - yes, you can do that in resources/CloudFormation template, however, there's potentially a lot of stuff to add (security groups, etc.), plus I have had issues before when locating the lambda in the VPC and having it just hang when trying to call AWS SDK methods (not in a current project, so a) i don't remember all the details, and b) it might have changed by now). My advice would be to use the default VPC for your RDS to get started, then once that works try creating another VPC, and stuff.
You also mention "deploy database scripts" -- are you asking about database initialization or migrations? Unfortunately, that's outside the scope of what I know that SLS can do right now (although, in fairness, there's been LOTS of stuff added recently).