How similar do terms have to be to connect them with 與, 與其，及其？ I often want to make my sentences short in order to pass our classroom exercise of writing a 簡體 abstract from memory in under 5 minutes. The biggest problem seems to be that I use 與，及其，與其，in inadmissible places.

The info we were given says, 與 can be used to connect nominal, adjectival and verbal phrases, with the first ones being the norm.

“与”较多连接名词性词语，也可连接动词性、
 形容词性词语，多用于书面语，书名、标题中常见。


Some people accepted 


  
  從該日起在此居住與唸書。
  


others wanted to replace 與 with 並。

The following was rejected explicitly on the grounds of the terms of 美國 and 美國的政治方法 being 不同類。


  2a.該研究美國與其政治方法。


Would it be better to use this?


  2b. 該研究美國及其政治方法。


On youdao there are sentences such as: 


  2c. 我们很乐意为这所房子及其庭院拍照。


Which I would assume to be exactly the type of 2b, particularly regarding similarity of terms (which I perhaps misunderstand). What about this?


  3a. 辜鴻銘不認可胡適這位新文化的帶頭人與其課程。


What about replacing 與其 with 及其?


  3b. 辜鴻銘不認可胡適這位新文化的帶頭人及其課程。
與： 和，and;
與其： 和他的， and one's;
及其： 还有他的，and also one's;
Back to your examples:


從該日起在此居住與唸書。// fine

2a.該研究美國與其政治方法。// wrong as the reason you said
2b. 該研究美國及其政治方法。// fine, [research on America and its methodology of politics].
2c. 我们很乐意为这所房子及其庭院拍照。 // fine, [take pictures for this house and also its courtyard.]
3a. 辜鴻銘不認可胡適這位新文化的帶頭人與其課程。// wrong, the same reason as 2a
3b. 辜鴻銘不認可胡適這位新文化的帶頭人及其課程。// fine, [disagree/disapprove the leader of ... and also his courses.]