I say leave that screen in place. The damper at the hood may help keep critters from coming directly into the house, but you really want to keep them out of the vent turbing and the T-top, as well. When you say "t-vent," I'm picturing something that looks like a roof jack for an attic vent with the opening and screening on the underside of the outer arms to the cross-bar on the tee. Around here, wasps & yellow jackets would be the biggest worry -- their nests could plug up your vent. Nasty to try to clean out. As for attaching the tubing, metal vent tubing comes in sections that plug together -- a slightly crimped end plugs into a slightly expanded end of the next section. The roof connection will be the same -- the top end slides inside the base of the t-vent. (May be a mite tricky getting it all to snap together with the roof unit already in place.) A couple of self-tapping screws through the vertical sides of the tee into the top ring of the tubing would be good if you can do that. The t vent may have screw holes already. Caulk would be okay -- but probably not ordinary vinyl painter's caulk because your local government code people might require a fire-rated caulk as you would with a chimney for a wood stove. It is readily available, just more expensive and more durable. Regardless, you also want to wrap and seal each duct joint with duct tape. (That's actually what duct tape is for.) For this application, you really want to use the aluminized tape instead of the "handyman's secret weapon" --- the common vinyl-cloth duct tape. The vinyl-cloth stuff just won't hold up very well in temperature swings you get in the attic and on the roof. If you have hot summers, that attic and underside of the roof will get very hot. Cloth duct tape softens and degrades in high heat. It also loses its grip in very cold weather. If you live in a place with cold winters, you also probably want to consider adding a second damper up by your t-vent. That mitgates the chilling effect of a cold column of air above your stove vent, particularly on windy days. This post was edited by JWVideo on Tue, Jan 28, 14 at 12:35

If your hood is on an outside wall, your not going to want to protrude through the roof too close to an overhang, especially if you are in cold country with ice dam concerns.You would have to elbow up to a higher location.In our area,a fire stop is required where the ducting enters the cieling/attic with any framing required to be 2" away from the duct.A fire stop is a sheet metal jack that accepts the ducting in the center.The fire stop is attached in your attic to cieling joists or blocking or both.The fire stop isn't so much for heat,as hoods aren't high heat,but are required to slow fire through penetrations.Your roof sheathing should be cut 2" larger than the ducting as well. The roof jack will easily cover that. A t-top roof jack is simply a jack that has a horizontal "hood" that keeps water out of the jack/ducting. You are going to want to study how other vents on your roof were flashed as well concerning your roofing, as an improper flashed jack is a guaranteed leak.If you use foil tape on the seams of your ducting,(my choice), make sure it is rated for heat.Good luck on your project! You might want to check in with your local yocals for venting requirements in your area. That's what they are there for and is a safer bet.

For the wall vent option, also consider the proximity of operable windows. Codes vary by locality, so you should probably call you local building inspector for clarification, but in my city in Northern California the vent must be >=3' from any operable windows. Folks above are correct that 90s in ducts result in pressure drop, but you're talking about a short run with a single bend, and you could always run a slightly larger duct if you were concerned about it, so I don't think the pressure drop from the single turn is a significant consideration because it's gonna work well either way. Primary considerations are: cost to install, how it looks, if smoke will find it's way back into house or otherwise annoy outside.

You did great with the hard duct angle and foil tape. That’s exactly what needs to happen here. The hard duct needs to terminate into the roof cap and be sealed. You may need to remove that and create multiple sections to make that happen since the duct below has been fixed by you sealing it to your hood. A hood can not terminate inside the attic, which this one does, because it isn’t properly connected to the roof cap. A duct can’t use flex duct. The small aerosolized grease particles that escape the larger filter trap will accumulate in the ridges of flex duct. That creates a fire hazard.