PE29 1TS is Coxons Close, PE29 1JL is likely the correct postcode.

node/100889557
What is this hotel called?

As noted on way/18835045 , cycle access as mapped in OSM "just stops" here on the motorway. Imagery suggests that a separate path exists across the motorway bridge. I didn't notice signage when last here (but wasn't looking for it); but the cycle route past the Millennium Hotel is signed.
Probably needs local knowledge or a survey to say what is best here.

"four bike parking bars present at these coordinates"
OSM snapshot date: 2025-02-27T10:33:49Z
POI has no name
POI types: amenity-bicycle_parking
#organicmaps android

"This building is called LDH House"
OSM snapshot date: 2025-07-08T15:45:36Z
POI has no name
POI types: building
#organicmaps android

This path will be replaced with another that starts 350 meters to the north on "The Street" It will come into effect when the signage is installed according to the Cambs County Council signs attached to footpath finger posts.

This wiil be the start of replacement footpath for the one that starts 350 metres to the south also on "the Street" I got this information from the Cambs County Council information affixed to the existing footpath finger posts. I have drawn the new route on openstreetmap, using CCC data and OSM's bing data. the charge takes effect when the finger posts are moved.

The Swan almost certainly closed: can FHRS confirm?

"Moved to a new location"
The place has gone or never existed. A user of Organic Maps application has reported that the POI was visible on the map (see snapshot date below), but was not found on the ground.
OSM snapshot date: 2025-02-27T10:33:49Z
POI name: Cambridge Academy of English
POI types: building amenity-language_school
#organicmaps android