#2 is standard industry wide, so you will have a hard time finding a PM who will do it for less. Also, in Houston, PMs cooperate w/ realtors to find tenants for you, so half of that may not even go to the PM, so keep that in mind. But even if it did, it is a tremendous amount of work finding a "Qualified" tenant for a rental. Basically, the property is like a mini-listing, only it's not for sale. PMs still have to photograph it, list it on HAR, respond to all the inquiries, weed out the non-desirables (which there are plenty of, trust me), show the unit, accept the application, screen the tenant, prepare the lease, coordinate receiving the funds, and handing off the home to the new tenant(s). I don't think one month's rent is in any way usurious for that amount of work.
#1 is definitely negotiable, but the main purpose there is to allow a PM to quickly respond to tenant complaints without having to try to reach you and get your approval on every little thing. This provides better customer service to the tenant (never forget, they are your customer, this is a business). If, however, you find a PM that is constantly abusing the trust you are giving them by allowing this, time for a new PM.
#3 is also negotiable, but may be area specific too. I know for my Indy rentals, I pay 25%, which includes an annual home inspection by the PM at the time of signing the renewal.
Lastly, I highly recommend @Jerry Ta. He is who I refer all of my investor clients to, does a great job, and I believe has very fair rates. I'd take him up on his offer.