Wire connection between ballast and lamp socket
No.  You need to wire the lamps according to the diagram.  What you propose does not match the diagram.  

On the yellow, the diagram says you must split the yellow wire to power both filament terminals on one "end" of the bulb.  

On the red, you must join 3 wires then split them to power both filament terminals on the other end.  

This splitting will take extra wires and wire-nuts. Use #18 solid wire rated 600V.  If you have spare length of ballast wire, you can use a little bit of that.  

This particular lampholder seems to have 3 holes per "side".  Note that 2 of those holes are "siamesed".  That is telling you they are interconnected to each other/ the same thing. Only connect to one of them.