I'm no expert, but I did build my own greenhouse last summer which included polycarbonate, and aluminum profiles.

If I use aluminum tape at the tops of the walls, do I need 'U' profiles at the top? Is it "either/or" and when do I use silicone sealant?

I used aluminum tape and u profiles. The top of the panel is where all the channel holes are, and you do not want anything getting in there. A u profile will protect the tape from tears or punctures that might otherwise allow water and dirt to get inside the panels. Use both tape and u profile for best protection. Silicone sealant is used to seal air gaps for better insulation, and to keep out rain. I used it along my ridgeline, between the wall and roof panels, and where the poly panels meet the wood walls. This all depends on your design, and you can always add it later if you find a gap somewhere.

How do I finish the bottom of the wall panels; 'U' profile; vent tape; silicone sealant? Wouldn't vent tape rot in the elements?

I used vent tape and u profiles. I'm guessing the vent tape is made from a synthetic material that will last a long time, but I don't really know. Again the u profile will protect the tape, so I'd use both.

Should the bottom edges of the roof panels be sealed with something more? They're going to get hit with driving rain which will run right up inside the polycarbonate panels.

Once again vent tape and u profile is what I used. Seems to do a good job keeping out rain and debris.

What are the 'F' and 'R' profiles used for and do they apply to my GH?

The f profile is used to secure panels at corners. You can drill through the flat part to secure the profile to a corner. I'm guessing you're planning on drilling through the panels themselves to secure them to the corner framing members, so there is probably no need for f profiles. The r profile is used to join two panels at a corner. I don't see any need for it in your design.

I would be sure to use the screws and washers made for polycarbonate panels. Don't overtighten them. I used a drill to start the screws, and then finish them by hand so as not to crush the polycarbonate.

Here's a picture of my greenhouse if it helps any.

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Keep in mind there is a difference between the profiles I used and the ones you're looking at. Mine are meant to be structural. They are made of stronger aluminum and have flat portions that allow the profiles themselves to be screwed down to the framing members. Then the profiles hold the panels in place, and the panels only need to be screwed down between profiles to keep them from bowing during high winds. The profiles you're looking at are mostly there to protect the polycarbonate edges. They are not secured to the frame (aside from the f profile), and therefore require the corners of each panel to be screwed down. Since you have ample framing, that shouldn't be a problem.

Also note that the site you listed offers two piece snap h channels. If your panel joints all line up with framing members, then the base piece is screwed down to the framing member, the polycarbonate panels are laid in place, and the cap is snapped on top. It makes installation easier, but is probably a bit more expensive.