Help with 1772-1788 Household record for Hånger parish in Jönköping

[Victoria Cihla]

Can anyone help with the attached household record for Hånger parish in Jönköping? 

Kärda (F) AI:3 (1772-1788) Image 79 / Page 141 (AID: v20706.b79.s141, NAD: SE/VALA/00207)
https://app.arkivdigital.se/volume/v20706?image=79

First,  I am not sure what the place name is at the top of the page, but I think it might be Byagården Hånger.

I believe the first name listed is Arfvid b. 1711.  who was married to a widow Ingier Larsdotter b. 1718 (19 Dec) 

The next line has a note of some kind which I can't read and it is associated with the name Anders? Arvidsson b. 1748 (2 Aug) married to a Brita Jonsdotter1760 (14 Dec)

Next is a daughter Ingier (presumably Arvidsdotter?) b 1752 with a son? lars b. 1788??

Next is a daughter Elin Arvidsdotter 5. 1756 (3 Sept) - she is also listed below with husband David Andersson 5. 1763 (19 Nov)

Last is daughter Ingierd b. 1752 is listed again with a note following her name (which I can't read)

I am not sure if I have this right, so any clarification or correction would be most welcome!

Thanks very much,

Vicki

[Ulf Berggren]

The last note is "tjenar", i. e. she is serving somewhere, probably as a maid.
The first note is too messed upp.
The farm name is correct, as is all your question marks.

[Victoria Cihla]

Hi Ulf,

Thanks very much for confirming what is correct and for telling me what the last note says!

I appreciate your help,

Vicki