1) Is a GFCI able to be installed right in the place of the old plate? When I unscrew the current outlet plate, won't there still be only two inputs for a two pronged cable?
Learn some basics.
1) One layer of human safety is provided either by that receptacle's third prong - safety ground. Or by a GFCI. GFCI obviously needs no safety ground to operate. So code permits a GFCI when a safety ground wire does not exist. And code also requires that stick-on label.
Either spend $hundreds to connect a new three wire cable back to the breaker box. Or spend $tens for a GFCI to replace the two prong receptacle. Inspect these in a hardware or big box store to understand this.
2) No earth ground can connect to any receptacle. Receptacle must have safety ground. That means it connects to the ground bar inside a breaker box - not to an earth ground rod. Receptacle ground is a safety ground; not an earth ground. Only the breaker box connects to earth ground - for human safety, transistor safety, and other reasons.
3) GFCI needs no ground to operate. To provide human safety.
4) A protector cannot shunt surges to earth via a receptacle safety ground for a long list of reasons. For example, the connection is too long (ie exceeds 10 feet) to earth. A plug-in protector also does not claim protection from destructive surges. Read its numeric specs. No protection claims.
5) You need surge protection for everything - not just a computer. Only protection that is effective for all circuits - two wire or three - is one 'whole house' protector that connects short to earth ground. Same solution is effective for all house wiring - 1930 or 2010 vintage. That means a protector that costs about $1 per appliance (compared to $tens or 100 times for plug-in protector). And connects to an earth ground that both meets and exceeds post 1990 National Electrical code.
One 'whole house' protector protects from all types of surges. One 'whole house' protector, properly earthed, means even a direct lightning strike causes no damage even to the protector.