Check out page 8 of
this.
When the serial input goes high, the program stops and the boot loader takes over. So you leave those 2 resistors in circuit and it won't happen.
Yes, pulling high means connecting to +v. You almost certainly don't even need a resistor.
Note that you'll have to check that whatever PICAxe you get supports the protocol used by this chip (SPI?). I think it's standard, but better to be safe than sorry.
My thoughts are as before on the subject of decoupling. KISS. make adjustments later if you need to.