Answer (1) only, not (2). Grammatically, I think you have to chose between the active voice in the continuous tense, and a form resembling the passive voice. The baby is lying on the ground - active voice, continuous tense. The litter is strewn everywhere - same form as the passive voice, though may not be technically a passive, not sure. Which one is correct out of the "-ing" form and the past participle form --- depends on the specific verb and context. I guess you probably just have to get used to English usage. Language, after all, is habit. Sometimes both are probably possible - the dog is stretched out on the rug; the dog is stretching out on the rug - I think both of those are OK. Often the version with "-ing" seems more active/intentional, and the version with the past participle feels more passive/unintentional, but that depends on idiomatic usage of each verb. Just learn lots of examples and copy them.

The two verbs to keep in mind, and their conjugations, are: lie, lay, lain (this is what you do on a bed) lay, laid, laid (this for when you put something, like a sheet, on a bed). Almost everyone has trouble with these two verbs. NEVER ever say "I lay down", or "the baby is laying down". Correct usage is: "I lie down" "The baby is lying down" "I am lying down" Your first sentence is correct. Your second sentence would be correct if only you had spelled the past participle of "lay" correctly: "The baby is laid on the ground." The British write "spelt" instead of "spelled".

The baby is laying on the ground

The 1st one is correct, because the verb “LIE”, when used in the Continuous form, gets like this. There are rules for the Continuous, when it comes to verbs. “When the verb ends with -ie, this ending is exchanged for -y and -ing is added. Examples: To die (morrer) – dying To lie (mentir) – lying”