We propose that the small GTPase that regulates filopodia formation in the developing axon does so by activating a kinase. The kinase in turn phosphorylates fimbrin thereby allowing filopodia to be formed. Turning on the GAP would result in rapid GTP hydrolysis which in turn would prevent phosphorylation of fimbrin. For the second part of the question, we need to explain how contact between the two cells could trigger changes in the microtubules. Microtubules are nucleated from the centrosome and, in the interphase cell, project out in all directions from it.
Microtubules display dynamic instability unless they are capped.
Monomeric tubulin can add to the microtubule only if it has a GTP bound to it. If hydrolysis catches up with the monomer addition leading to exposure of GDP-tubulin at the end of the microtubule, the microtubule undergoes catastrophic breakdown. Microtubules can also be capped by proteins. Capping proteins protect the microtubules from catastrophe and thus turn dynamic microtubules into stable ones. If the capping proteins are localized to a particular part of the plasma membrane, they can also appear to orient microtubules toward that region because they capture and stabilize the microtubules in that direction while the microtubules pointing in other directions are not capped.