המקיים קוצים בכרם - The crux of the disagreement between R' Eliezer and the Sages is whether something which is cultivated in only some places can render a vineyard כלאים.  Thistles were cultivated in Arabia as fodder for camels, and so R' Eliezer held that they were כלאים whenever they grew in a vineyard, while the Sages said that it would only be אסור in those areas where it was cultivated.

והקיסוס - This is the spelling more often used for this plant (other spell it קיסום); it is apparent from רש"י in סוכה, דף ט עמוג ב that this is a climbing vine like ivy.

ושושנת המלך - While the מהר"י בן מלכי צדק and רע"ב say that this is a type of rose, the ר"ש and others disagree, as roses are usually classified as a מין אילן (we say בורא עצי בשמים on their aroma) and not מין זרעים as this is classified here.

וכל מין זרעים - The משנה ראשונה says that only cereal grains (תבואה) and some say vegetables (מיני ירקות) are כלאי כרם מן התורה (with certain exceptions mentioned earlier in the מסכתא).  The ראב"ד is גורס this clause without the word וכל, but says that these are not כלאים because they are not cultivated, not because they are not תבואה.

והקינרס - This is identified as the דרדר mentioned in פרשת בראשית, ג:יח and which is often translated as thistles; note that the globe artichoke is a species of thistle.  The ר"ש, citing the בראשית רבה, explains the etymology of דרדר for artichoke as being a play on the words דרי דרו, or layers upon layers, which is similar to the constitution of an artichoke; the תיו"ט in עוקצין, ג:ב gives a similar explanation, although he appears to raise the possibility that קינרס and קוצין are often confused with each other.