I don't think your user name is too similar, no. If it invoked cats in any way, then we might have a problem, but as it stands, I doubt you'll confuse anyone. (preparing to be proven wrong in 3... 2...)
Seriously, though, welcome to the Board! Have an electric trident! Electric as in it shoots lightning from the tips, not as in it needs batteries. It's powered entirely by ill-defined magical energy, so you won't need to worry about charging it.
And to answer your questions:
1) Agents like to gripe about things. It helps get out some of the frustration that they feel after watching badfic mangle their favorite fictional worlds, which isn't always dispelled when a Sue gets a sword through the chest. Talking about getting raises and complaining that there's barely any time between missions any more are common manifestations of that. They're exaggerating about the lack of time, by the way. There's plenty of time between missions, as evidenced by the massive number of between-mission interludes that have been written over the years. It's just that the console could go off at any moment, so a lot of Agents don't feel that there's much chance to do anything.
As for the actual purpose of the money, I don't think anyone is entirely sure, but it might not be out of the question that the money could be used to purchase things at HQ's internal businesses, such as the Supply Depot or Rudi's Pub, or to purchase things from within the various continua that the Agents travel to. I doubt the Agents would ever have too high a need for the latter unless they were stranded there or something, though. Ailavyn Siniyash's idea about the Cafeteria once dispensing good food for money may be true as well. It sounds like something they'd do.
2) It's not really something that anyone tends to consider, usually, since there are a few dozen different species of Flowers and they all have their own individual ways of performing most tasks, moving around not being an exception. I'm pretty sure that a large potion of them drag themselves around on their roots or pull themselves forward with fronds, but there are some that don't have any appendages to speak of, or those that are simply too large to make doing so practical, plus individual personality quirks that might affect their choices. Maybe some would find pulling themselves across the floor demeaning, or some would prefer alternative options to the obvious ones. Knowing how the Flowers can get, I expect that at least a few push themselves around on some sort of skateboard/wheelchair contraption because wheels can go down long hallways faster, or even self-levitate with their psychic powers. I think that the Bracket Fungus could self-levitate, but admittedly I'm not entirely certain where I'm remembering that from.