Well, I am not sure because if you say in #3 pedal is "soft" at first start I would be tempted to consider an "air in the system" problem (like I have, I have read and re-read the RAVE procedure but I can't get it right, alone is nearly impossible it seems), but the pump running at each press it could be a separate problem.
As StrangeRover has said, it is an expected matter if life of the canister goes out.
You should make sure as Richard said, you got no air in the system at all.
Air in the brake system can come from the ... air :-) but it could be also not just air: brake fluid is hygroscopic and it does attract moisture and water molecules in the air (there is a membrane in the reservoir to equalize pressure), water/moisture content which besides lowering boiling point of the fluid and diminish brake performance, plays havoc with caliper pistons and seals "from inside". Considering caliper pistons have already a rough time from crud "from the outside" which can get past the caliper seals, once they get rusted you can expect more trouble, and more expensive as well :-)