About the only square drive (Robertson) screws available in my part of the US are wallboard screws, for mounting "plasterboard" to walls, and "deck screws" for wooden decks (housing - not boats). Both of these are relatively low-torque applications, with the square drive slightly better with respect to retention on the driver than the more common Phillips. The better retention of the screw on the driver with the square socket has some advantage for power driving with manual tools.

The Phillips and PosiDrive sockets are slightly different approaches to clearing the misfit at the center of the screwdriver due to the "fillet" between the "blades." US standards generally assume forge-formed screw heads and screwdriver blades, and this method of manufacture slightly favors the Phillips for manufacturing cost. The PosiDrive is theoretically better adapted to cut slots in either or both of the screw head and/or screwdriver, although forge-forming can get pretty much the same results. For properly fitted tools/screws there's little real difference between the two, but the best of tools cease being "properly fitted" after fairly short use.

PosiDrive screws are virtually unknown in the US market so far as I've seen. Phillips and Square (Robertson) bits are easily available.

Allen Head (hexagonal socket) screws are much used in machinery and to some extent in US autos, and are adaptable to higher installation torque than any of the above. They also have better retention on the installation tool. In US "standard parts" Allen Head fasteners are seldom found at lower grades than SAE 3. In US autos, the Torx head is the preferred kind for "power driving" due to retention on the tool comparable to the Allen but also somewhat easier "machine insertion" of the tool into the fastener head. Although Torx advertising claims higher driving torque capabilities than for the Allen, few applications install either kind to high enough torques to really make the difference of much significance. The Torx bits actually are a little easier to find here than Allen bits for use with power tools, although Allen "key" wrenches and T-Handles are easy to find.

Where it is necessary to develop the full mechanical strength of a "screwed" fastener, the external hex head usually is the way to go, although designing a fastening to take full advantage of one or another style of machine-strength screw is a "skilled art." True "High-Strength" joints nearly always require both bolt and nut, and nearly always incorporate an additional retention or locking device of one kind or another. Internal Hex (Allen) or Torx screws do generally allow closer bolt-to-bolt spacing than external hex heads, so they're sometimes used in highly stressed joints where uniformity of stress loadings is more important than individual fastener strengths, and are somewhat more often used in "threaded holes" without separate nuts.

As to the plastic push-pins, it's been quite a while since I've been under the sheetmetal in a Ford, but I'll take a chance and vote with Joe O: The most common kinds are intended for one-time insertion¹ and should be replaced with new ones if you have to take them out. You'll be able to tell for sure once you get the (pieces of the) first one out.

¹ In "specification assembly" to US Government and Standards Association rules, Nuts with friction-retention devices cannot generally be removed and replaced more than about three times - with specific inspections if considered for re-installation even once. Nuts with Deformed Thread retention features are about the same, but less likely to pass the inspections. Split lockwashers are (it says in the rules) always to be replaced. Toothed lockwashers are not properly used for "retention" so they can usually go back in five times "if they look good." Castle Nuts can be reused, but the cotter pins (or wires) should always go in new (if you really want to fussy about it).

John