Relationship between auto-ignition temperature with pressure and fuel
1) One could argue that yes. All other things being equal, larger molecules will clearly have lower vapor pressures at the same temperature so it is reasonable that there is a limit at which the fuel-air mixture is too lean to support autoignition.

2) After reading the paper I can only conclude that they are referring to the above idea that autoignition temperatures increase for larger compounds due to the need to increase the vapor pressure to reach an appropriate fuel concentration that supports autoignition.

3) Larger volumes have lower surface-area-to-volume ratios. The lower surface area means a the walls of a vessel play less of a role in the combustion chemistry leading to a lower AIT. These surface effects are detailed by Babrauskas with references to those who have observed this.
 

Babrauskas, V.
 of Fire Protection Engineers, S. (Ed.)
 Ignition Handbook 
 Fire Science Publishers, 
2003