Amp is plugged to the wall, why use a conditioner?

The two main reasons folks give not to plug an amp into the conditioner are:
The conditioner limits dynamics, and punch of an amp The conditioner creates a gain in clarity, at the expense of mid to low bass.

These in the minds of folks who say do not use a conditioner on the amp, are more important than the gains in other areas (if you do use a conditioner for the amp.)

Since I like the sound of 'my' amp on 'my' conditioner, I use it on the amp.
(Bryston 4B-SST2 on a Furman REF20i via Pangea AC9 powercord)

And since all the discussion in the world will NOT tell you if having the amp on or off a conditioner will be what you like best...

If you really want to just do what others tell you you should do, then the majority say no conditioner for amp.

If you try it you may (or may not) find you like it (or not.)
It's your ears.

For your questions: No ,having the other stuff plugged into a conditioner will not be 'messed up' by having the amp straight to the wall.

The conditioner may or may not help with the hiss.

Depends on the conditioner and the amp(s). Also, before doing anything else, I'd have dedicated lines installed just for the stereo system. The usual recommendation is for 20 amp lines. My Tice Power Block III put the lie to the idea that conditioners compromise power amps -- surprising the heck out of the guy who built my amps-- and the more expensive PS Audio P10 makes them sound even better. (Two of my audiobuddies also have that particular Tice, by the way, and wouldn't be without it.)

There are a lot of GOOD reasons to use a line conditioner. Irrespective of audible effects, a good line conditioner like the Furman products filter a lot of line voltage transients that can damage your equipment. These transients over time can damage sensitive transistors and amplifiers. Not sure if tube equipment is as sensitive, by it only takes a nanosecond transient to destroy solid state devices.

Some products can provide power factor correction, and provide line capacitance that helps the transient response of power amplifiers. I use a Furman Power Factor Pro on all my equipment, particularly the power amps. It reduces line voltage sag when transients hit the power amp. I use another one for the low power stuff like CD players, A/D converters, preamps and the like to isolate them from AC power effects caused by the power amps.

Some line conditioners also can regulate the AC line to smooth out brown outs. I have used the Furman AR-15 which actually has a switched transforment that keeps the output at 110 VAC even if the line drops to 90 VAC or rises to 130 VAC. I have found these can be audible, however, so I only use them on computers and other electronics, not my audio components.