Yes I believe the plan is for 2tph Henbury-Bristol of which 1 continues to Portishead, similar to the 2tph from Avonmouth of which 1 continues to Weston.
Yes, and some groups do keep suggesting it.
Running more trains north of Avonmouth means greater closure times for the level crossings allowing access to the docks. It might be possible to put up a steeply graded bridge for the King Road Ave LX but there's not a lot that could be done about Gloucester Rd immediately north of Avonmouth other than moving the northbound platform to the other side.
Terminating trains at Parkway from Henbury involves the very awkward junction at Stoke Gifford/Parkway itself, and consumes valuable platform capacity at Parkway. And running more traffic through Hallen Marsh junction means freight is forced to take ever slimmer pickings.
I don't really see a big problem with one extra train per hour in each direction going across Avonmouth Station level crossing (Gloucester Road, next to the station) and St. Andrews Junction level crossing (King Road / King Road Ave, next to the signal box that controls all the crossings, the main port access).
In the past, Avonmouth Station crossing was really busy, but since the port decided to make King Road / King Road Ave the main entrance / exit, Avonmouth Station crossing is now quieter and is mostly used by locals and people visiting the local shops and businesses. It's a mix of both pedestrian and vehicle traffic.
St. Andrews Junction level crossing can get busy, but current crossing closure times are much reduced since the token section was replaced with more modern signalling. From 1988 through to 1993, the signal box was the start / end of the token section to Severn Beach. Every train stopped on or right next to the crossing to obtain or return the token to the signaller.
So in comparison to that, the extra two to three minutes for each extra train is not significant. And the roads are plenty long enough for the traffic that does have to queue. There are very few pedestrians that use this crossing.
Oh, and sometimes the traffic queues due to the port police checking trucks, the checkpoint is just beyond the level crossing.
A relief line was added to Stoke Gifford West junction (just West of Bristol Parkway station) when the junction was relaid only about eight years ago. This was to make operations easier for down trains from the new west/southbound platform (platform one). However, this relief line is only available for trains going in the Filton Abbey direction.
The limitation is that the connection to the line going towards Henbury (or beyond to Avonmouth) is a single line / lead junction off the main lines. So how practical it would be to have a new passenger service using this depends very much on if there are enough suitable gaps in the existing main line services.
Since the bulk handling terminal hoppers closed (after the last coal train to Aberthaw power station, the power station having closed on 31 March 2020) there hasn't been a very intensive freight service.
There are the trains that go to / from the docks (via Holesmouth Junction, just north of St. Andrews Road Station) and the trains that to go / from SERC (Severnside Energy Recovery Centre) which is a connection off the Severn Beach line. Three years ago that was two trains per 24 hours (normally at least one movement was at night) for the SERC trains.
There may be some freight trains that now use the sidings that were originally part of the bulk handling terminal. Maybe for transfer to road transport.
Unless something has changed in the last couple of years since I was last in this area, that's all the freight that is running.
Avonmouth-Henbury is quite an indirect route through mostly unpopulated areas. I’d get the crayons out and go for a new build line cutting the corner, parallel to the M5 on the south side with a station for Lawrence Weston, though that would need serious money and probably need to branch off from Shirehampton area, not Avonmouth.
It's not very far via the existing railway line between Henbury (site of the proposed new station) and Avonmouth station, so there is no chance of a new line being built. In-between Avomouth and Henbury you have the current (open) St. Andrews Road station (serviced by Severn Beach trains) and the closed station at Chittening (some of the upside platform still exists, it's near where Smoke Lane joins Chittening Road). This did serve the industrial area rather than houses. The industrial area is now larger than it was.
I'd keep the existing Cardiff-Bristol-Bath-Portsmouth semi-fast (also calling at Filton), which would serve some of the cross-Bristol flows. Then add 2ph (or 4ph if there's space) Bristol-Bath-Westbury as a metro service alongside it. The Gloucester services would terminate at Bristol.
Keep in mind that the line between Bristol and Bathampton Junction (just east of Bath) is already very busy. It's likely near capacity at certain times. And there isn't really any realistic way of easily adding capacity.
I think at least 1-2tph from Weston-super-Mare should actually start back at Taunton, so Bridgwater + Highbridge have more services. This overall service plan would require other infrastructure upgrades though, including reinstating the down loop through Bedminster & Parson Street, and having the up loop allow trains to call at Parson Street, which would allow a larger window for fast services to overtake a stopper, and/or keep the Portishead trains separate for longer. Then redoubling both WSM chords and allowing the bay platform to return to proper use would help too, along with the east-facing Taunton bay (P6) being resignalled for direct access.
To be pedantic, what you are calling loop lines between Parson Street Junction and BTM are what BR Western called Relief lines. Indeed, Network Rail still call the existing "loop" up line the Up Relief.
I've not heard of the "Weston loop line" being called "chords" before.
Reinstating the Down Relief line is on the Network Rail (wish) list of "would like to have" improvements, as is doubling the line between Worle Junction and W-s-M (this would include the reopening of the bay platform), plus doubling the line between W-s-M and Uphill Junction. But currently there is no money to pay for any of this.
Also in addition to those that you listed, doubling the part of the existing Portishead line between Clifton Bridge and where the current line is doubled at Ashton would be helpful for train regulation. And ease the operation of Ashton level crossing.
Bringing platform 2 at BTM back into passenger use (requires a change to the track layout) would help to reduce platform congestion for trains from the West that terminate here. Reinstating a West connection for platform 3 so that it becomes a through platform would also help (again the track layout need s changing, the removed points needs to be put back in).
If St. Anne's Park station is ever funded for reopening, providing relief / loop lines between this possible new station and BTM East Junction should also be considered. Although because some new bridges would be needed, this would be rather expensive.
For Portishead itself, 2tph will probably need a loop somewhere on the branch in addition to the one around Ashton Gate, either at Pill station, or in an attempt to avoid expensive accessibility upgrades, a dynamic loop west of the station.
The current new design is for a dual track through Pill station. One line for freight to / from Portbury docks and one line for passenger trains to / from Portishead. So although not a loop, it does ease mixing of the two services.
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