Use your grout saw to extract the damaged grout from between the porch tiles. Scrape the blade forward and back over the grout, extracting all the damaged or loose grout, leaving the rest in place.
Use the hose on the shop vac to pull the pulverized grout out of the lines.
Use your razor knife to cut away the old caulk from around the perimeter of the tile surface, where it meets the house. Cut it out lengthwise, running the blade along the top and bottom edges of the caulk line.
Spread grout over the areas of tile where you extracted the grout, using a grout float to scrape the grout over the lines diagonally.
Let the grout sit for 10 minutes. Wipe off excess grout with a damp sponge and let it set for 24 hours.
Put a caulk tube in your caulking gun. Cut off the end of the tube at a 45-degree angle, using your razor knife. The hole should be about a quarter inch across.
Set the tip of the tube at one end of the tile's perimeter--against the house, where the old caulk was. Hold the gun at a 45-degree angle.
Compress the caulking gun trigger and pull the gun slowly backward along the edge, letting the caulk seal the line between the tiles and the house. Make one smooth, continuous bead from end to end.
Wet your thumb and run it over the caulk line from end to end to smooth it out. Repeat for the edge of the porch.