'cot' and 'camp bed' In American English, a cot is a narrow bed for an adult. It is made of canvas fitted over a frame, and you can fold it up. You take it with you when you go camping, or you use it as a spare bed at home. In British English, a bed like this is called a camp bed.
Across is a preposition. It describes the relationship between two persons, places, or things. It is sometimes used with the preposition from. Example: That house is across the street. Cross is most commonly a verb or noun. Crossed is the past tense or past participle of the verb to cross.
The name is not important althought the most accepted term is phrasal verbs. The preposition can be a preposition or and adverb. Again this is not important at all. You can call it a preposition, a preposition or an adverb. On this site we use the word preposition because it covers both prepositions and adverbs. The important thing is being able to understand and use phrasal verbs.