I really wish AWS would allow users to cap billing. Something that freezes all AWS services if the monthly bill exceeds X would make me a lot more comfortable when experimenting with AWS.
Lightsail is dumbed down to the point of basically being worthless. There's really no reason to use Lightsail over Digital Ocean.
(Note: I have no investment in the company)
Without wishing to be too promotional, you can set a trigger to shut off EC2 when a cost threshold is reached. You can currently automate shut off of RDS but not yet from a cost threshold (that will be available shortly).
TLDR: we can do a lot of what you ask but not all of it.
Feel free to reach out if you'd like more info.