The easy answer is, no. None of the first sentences are correct, except for the first sentence in the first set.
This I have seen and heard regularly. The rest of the sets, numbers 2 and 3 are correct.
Edited: 11 December, 9:25pm EST
I have searched and searched, but have not found a single source that will allow for any wiggle room under the Most High Law of Subject-Verb Agreement. There is never considered a subject, so the subject is, of course, the collection of objects on the table, and regardless of how they are listed, it is a plural subject. I have no grammatical foot to stand on, hence Newton's Law of Universal Gravitation applies.
However, in usage, I will plead my case to Psycholinguistics, wherein research has generated theories in abundance about the architecture and mechanisms of sentence comprehension. At what point in reading does information become available to the reader? Issues such as "modular" versus "interactive" processing have caused heated theoretical rifts in the field.
Sentences are read in separate modules with which the reader interacts. but which have limited interaction with each other. While I generally hold to an interactive theory of sentence processing, in this case I am admitting that the modules are not playing well together at all. In an effort to avoid tedious squabbling, one grabs hold of the first module and deals with its behavior, whilst allowing the others to run amok. Admittedly this is poor parenting on the whole, but what's a person to do? One can listen to the cacophony only so long before becoming overwhelmed.
I place some of the blame on the misbehaving modules. Perhaps it is genetic, as a module does not come into a sentence as a tabula rasa. If the modules would cooperate and line up nicely, there would be little problem.
I summarize that the allocation of attention and the misbehavior of the modules makes this an impossible situation, one that defies the Most High Law. I throw myself on the mercy of the Court.
John Q Public is the Judge.
Merriam-Webster's first definition for box is 'a rigid typically rectangular container with or without a cover', but 'box' is also commonly used for 'cardboard box', which is probably what you are packing the samples in.
The reason we ever felt compelled to say 'cardboard' before 'box' is that the word actually derives from the box tree, suggesting that boxes are made of wood.
box (n.) Old English box "a wooden container," also the name of a type of shrub, from Late Latin buxis, from Greek pyxis "boxwood box," from pyxos "box tree," which is of uncertain origin.
Carton, on the other hand, derives from a word meaning 'paper':
carton (n.) 1816, from French carton "pasteboard" (17c.), from Italian cartone "pasteboard," augmentative of Medieval Latin carta "paper" (see card (n.)). Originally the material for making paper boxes; extended 1906 to the boxes themselves. As a verb, from 1921.
Dictionary.com defines 'carton' as 'a cardboard or plastic box used typically for storage or shipping'.
So a 'carton' is a type of 'box', but as your own research has shown you, boxes can be made of harder materials than those typically used to make cartons. I wouldn't insist that you use one word or the other, but sometimes the slight difference in their meanings can be useful.
In shipping large quantities of packaged items (smaller boxes) within one large box, you might choose to differentiate between the contents and the container by saying that you are packing a number of cartons (less durable boxes) into a box (suitable for shipping).
Best Answer
The noun removal is being used as a noun adjunct to service where it acts as an adjective, describing the service.
It is normal to use the singular in this case, even in with words that are generally always plural, hence "a trouser press" rather than "a trousers press". There are exceptions, particularly in British English, but they're mostly derived from forms that were originally using the plural possessive (e.g. "writers' group" becoming "writers group") rather than starting out as a noun adjunct. They're also something that many would criticise as bad grammar.
So we have coffee shops, not coffees shops, video libraries, not videos libraries, pet hotels, not pets hotels, and removal services, not removals services.
The other way to look at it is to just look at what people do. While a google search can find some people using "removals service", but many more using "removal service". Meanwhile this chart compares uses of the two found in books, the blue line is "removal service" and the red line "removals service", which is zero throughout: