谢邀！粗略读了下原文，试答如下：

第一个问题，主语宾语相关必具性状语，如何与可选性状语区分。                        

这个问题提的有启示意义，按夸克的说法，(i) Except for the obligatory adverbial in the SV A and SVOA types , adverbials are optional:那么记住这几种必具性状语的使用范围就可以了。A.主语相关的多指连系动词be，get，turn等后面的表语成分，在是介词短语或副词的时候，有时候也被称为状语。比如She was in a hurry. The chrysalis slowly turned into a butterfly.（obligatory predication adjuncts） B. 某些不及物动词必须跟介词短语或副词(表示地点，方向，时间）等一起才能表达完整的意义。常见动词如go, last, live, lie, extend, lead, stretch. 我们可以说The road goes (leads)to Beijing. 但不能说 The road goes（leads）.语义不完整，语法不正确。但对这种状语的称呼不必太过在意，各种语法书常有不同叫法，比如However, some intransitive verbs co-occur with a constituent that expresses location, direction, or time, and which is obligatory in the sentence structure. This constituent is called the Adverbial Complement  C.而在有些动词如put, place, bring, drive , get , lay, 等使役动词的宾语后面，介词短语或副词表示地点、方向、目标等意义时，这些状语不可缺少，夸克称之为宾语相关必具性状语。She placed the baby on a blanket in the living room. (fict†)                                                        //Put a note on my door. (conv) // [You could take it to the kitchen] [and put it under the grill of the electric cooker [in order to get it hot]], without knowing why it should be hot. (fict) 这种状语其实和宾语补足语类似，The adverbial in the SVO d A pattern most typically expresses location. Unlike adverbials in general, it cannot normally be moved or be dispensed with (without making the proposition incomplete). It differs from ordinary locative adverbials in that it does not specify the circumstances of the ‘placing’, ‘putting’, etc., but rather describes where the referent of the direct object ends up.

上面引自《Grammar of Spoken and Written English》一书，直接宾语后的介词短语被称为obligatory adverbial而宾语补足语被称为object predicative，也有不少语法学者把它们看作宾语补足语，这样就避免了所谓的必具性状语和一般性状语的区分，而只需要记住哪些动词是复杂及物动词即可。如《Analysing Sentences An Introduction to English Syntax》2016第四版把宾语补足语也称为object-predicative 并同时举了几个例子：

[48] Jack finds his own jokes extremely funny. (AP)

[49] They made Stella their spokesperson. (NP)

[50] Liza put the liquor under her bed. (PP)

其实该书的作者早在夸克语法大全刚出版就提出了这种更为简便的分析方法，在《The Linguistic Structure of Modern English》（2010）一书中P.209：The object complement characterizes the object in the same way as the subject complement characterizes the subject: it identifies, describes, or locates the object (as in We chose Bill as group leader, We consider him a fool, She laid the baby in the crib), expressing either its current state or resulting state (as in They found him in the kitchen vs. She made him angry). It is not possible to delete the object complement without either radically changing the meaning of the sentence (e.g. She called him an idiot => She called him) or making the sentence ungrammatical (e.g. He locked his keys in his office=> *He locked his keys).同样也把表位置的介词短语看作了宾补。

还有《English: An Essential Grammar》2019，第三版，称宾补为 object complement，并给出了He put the milk in the fridge.这个例子，而在以前的版本并没有这种表示位置的例句。

第二个问题，至于无动词分句，语法界并无统一定义，不必过于执着，像Aarts 更是喜欢用small clause这个概念，并且把无动词分句非限定分句都包括了进去，甚至宾补结构也被纳入。无动词分句原来被Kruisinga 1932, Zandvoort 1969称为free adjuncts without a verbal form, Poutsma 1904 称这些结构为nominal clauses, 当时All of these authors, however, discuss verbless clauses as possible realisations of adverbials, ... 1972年，夸克等人在《当代英语语法》对无动词分句其它不同功用的可能性进行了讨论，认为它们极其类似非限制性关系从句。后来《英语语法大全》里进行了细化陈述，但都强调无动词分句的状语作用，所以，它们不是句子结构的必具成分，这也能从She gave us our coffee black.看出，black可省略而不影响结构和基本语义。（ She is here.这是一个标准的限定句，同时就是夸克所说主语相关必具性状语。也就是第一个问题的A类，其实看作主语补语就一劳永逸了，和名词形容词作主语补足语即表语一样，这样也就没有是不是必具性状语这个问题了。）夸克他们没有对这些结构作为限制性关系后修饰语的情况进行讨论。1989年Pieter de Haan 在其著作《Postmodifying Clauses in the English Noun Phrases》提出restrictive relative postmodifiers的概念，“Verbless clauses can fulfill different functions. They may be used as modifiers. According to De Haan : verbless clauses…can not be looked upon as phrases, they are called verbless clauses not merely because they can be extended to finite relative clauses, but because of the fact that their constituent parts relate to each other in ways that can not be described in terms of phrasal constituents (modifier-head, etc.), but only in terms of clausal functions .”但是无动词分句后来范围无限扩大，感觉所有进步了细化了的东西，一下又被带回了混沌初态，同时附和的人好像也不多。夸克的语法一是比较早，二是可能也不认同此观点，比如当代英语用法/英语语法大全的著者Leech等1975年就定义了无动词分句，在2021再版的《Grammar of Spoken and Written English》中仍然认为As with supplementive clauses, their role is usually adverbial.

至于对语法结构的理解和判断，第一要务是先充分理解掌握这些词汇各自的语义和特殊用法，不能照猫画虎，依此类推，这才真正的语言功底，二是语境，词汇和语法结构显示可能讲的是什么，而语境帮助确定具体语义。词汇/语法/语境/逻辑综合判断，夸克语法中例句I found the letter in the kitchen. I typed the letter in the kitchen.语义判别就不说了，只说在是宾补的情况下能不能看作verbless clause，如I found him in the kitchen，首先，他们是句子的必要成分，宾语+补足语，它们的整体意义要和谓语动词一起理解才完整，分开成句语义经常无法衔接，二是，我们经常有加上to be 的情况，I found him to be in the kitchen.那就明显不符合无动词分句的定义了。第三，更何况，宾语补足语还有很多带有非限定动词的情况，这样，把一种不固定的个别现象单独视为verbless clause, 也会引起分类的混乱，徒增负担。但是你非要说这是verbless clause也不乏同行者，大咖Bas Aarts就认为(16) Martin considers [Tim a creep]. (17) Phil deems [Henry foolish].The bracketed clauses have been called verbless clauses , but a more recent term, which we will adopt in this book, is small clause (SC) . Small clauses are clauses that lack an overt verb, but can be said to contain an implicit verb be. 《ENGLISH SYNTAX AND ARGUMENTATION》2024，所以不用那么纠结。

第三，双宾动词改为介词引出间接宾语，SVOA 夸克语法基本是看作状语的，此种情况下的介词短语作状语是必具性的，但是他同时又介绍了We later (16.56.ff) consider an alternative analysis in which the to-phrases and the for-phrases illustrated above are described as prepositional objects, and are regarded as grammatically equivalent to indirect objects.这种也有语法家视为复杂及物动词的必具性状语，如whereas in John gave a bunch of roses to Jenny one might hypothesise a complex-transitive verb give in the clause pattern SVOA (as suggested by Stan-dop (2000)。这和剑桥语法的处理基本相同。

第四，夸克所说的不定式不能用于被动语态我理解是指不定式不能做主语改写为被动语态，  I told/advised/persuaded Mark to see a doctor.[ I ]

~ Mark was told/advised/persuaded to see a doctor. [2]

Like [D3] verbs, [D6] verbs form only the first passive exemplified in [2] above: we do not find *To see a doctor was told Mark. The following verbs belong to this class:

至于最后那条注释，不明白所指为何。

啰嗦一大堆，希望能稍解疑惑。

一家之言，仅供参考！