This one is tough, since we normally expect the prepositional case to end in е and sometimes я. But кровать is a feminine noun that ends ь. In the prepositional case, feminine nouns that end in ь drop the ь and replace it with и.
For more details, See Ben Clark "Russian," third edition, page 114. This is the best Russian book for beginning to intermediate students for grammar.
Yes it is. But there is a small feature "Лежа́ть на крова́ти" - "lying on a bed" (lying on top ) means that one is relaxing there.
"Лежа́ть в посте́ли" - "lying in a bed" (under the covers/sheets) means that one is going to sleep or sleeping etc.
"Посте́ль" means that a bed is covered with sheets etc.
"Стели́ть посте́ль" / "расстила́ть посте́ль" - the bed spread, to cover the bed with the bed sheets.
But "лежа́ть на посте́ли" usually used for a request not to do so (for example parents ask their children) "не лежите на постели" or "не сидите на постели". These choices mean that (for example) children are sitting or lying on the bed on the bed sheets in their casual clothes and if they want to lying (/sitting) on (or in) bed they have to change their clothes
- Probably because "На кровати" is a place, the speaker and listerner usually know what place is mentioned.
- Because "На кровати" is first, and thus the speech is about bed, like "What is on the bed? A ball is on the bed", and not "Where is the ball? The ball is on the bed"(That would be "Мяч лежит на кровати").
I hope I made it a bit more clear.
From the tips and notes for this section:
Note that even in the present Russian still uses verbs like "is situated", "stands", "lies" way more often than would be considered normal in English. ... You don't have to translate verbs like "to stand" and "to lie" literally when they refer to objects. Such use is not, by a wide margin, nearly as standard in English as it is in Russian: На столе́ стои́т ча́шка. = A cup is ("stands") on the table. In English "to be" is perfectly fine, so we accept that.
Лежит is a verb meaning "is lying," and здесь points to a specific location meaning "here." If I used здесь in place of лежит, to me, На кровати здесь мяч would sound like On the bed, a ball is here... or something.
It feels a bit redundant to indicate the location здесь, when I have already indicated the location на кровати. You could say Здесь лежит мяч, though, and leave out the на кровати altogether. (Or even Здесь мяч, if you didn't want to talk about the lying position of the ball at all.) But I don't know that I would use both На кровати and здесь while leaving out лежит.