the group set out for Athy having had an enjoyable, interesting and fun weekend

Question

However, on landing all was well and the group set out for Athy having had an enjoyable, interesting and fun weekend. https://www.lexico.com/definition/fun

This sentence is an example listed as one of adjective "fun". I cannot understand the part after "and". Before "and", the subject is "all" and the verb is "was". 1) After "and", what is the subject?

[The group]subject [set out]verb [for Athy]prepositional phrase [having had an enjoyable, interesting and fun weekend]

If this analysis is right, the meaning is "the group started a journey to look for Athy"??(Does "set out" mean "to start a journey", doesn't it?) Then, 2) who had an enjoyable, interesting and fun weekend?? The group or Athy? 3) If Athy is the one who had an enjoyable, interesting, and fun weekend, aren't we supposed to put a comma before "having"?
Or, is it just "the group" who had an enjoyable, interesting and fun weekend? I cannot identify 4) what is the grammatical role of "having had an enjoyable, interesting and fun weekend". adverbial participle clause? postmodifying participle clause? gerund clause?

Thanks in advance:)

Answer 1

Set out for means to start a journey towards a destination, yeah - Athy is a place.

However, on landing all was well and the group set out for Athy.

When they landed (by plane or boat, probably) everything was fine, so they set off towards Athy. The group is the subject of the sentence.

Having had an enjoyable, interesting and fun weekend is a participle clause. It's giving extra information about the group, and their experiences. They had a fun weekend, and the present perfect form implies that has some effect on the present - they were in good spirits, they'd had a good experience, etc. It's describing their state as they set out.

This ties back to the first part: However, on landing all was well. This implies that there was a potential problem - maybe they thought they'd be unable to continue their journey, or there would have been a cloud hanging over their heads during the rest of the trip. However things were fine, so their weekend had been fun and enjoyable (with no problem), and that was the reality for them as they set out to Athy.

Kind of a complicated example for fun! Also the technicalities of grammar terminology aren't my strong point, so you might get a better breakdown of the structure and function of different words from someone else!