Yes, it can be both an adjective and an adverb. 1. I stay home barefoot all the day long<----is it correct and natural It's almost right. 'Stay home barefoot' is OK, but the time expression should be 'all day long' (without an article). 2. I stay barefoot home all the day long<---what about this order? No. 'Stay home' is a set phrase, so it shouldn't be separated. 3. I am barefoot home all the day long?<---what about this? No, for the same reason as above. 'Home' should be next to the verb. 4. I am often barefoot. <--- correct and natural? Yes, it's OK. You could say that you 'have one bare foot' if for some reason you have a sock on one foot but not the other. The adjective/adverb 'barefoot' implies that both feet are bare. We also use this word with verbs of movement eg, 'Barefoot running is a popular trend' (adjective) or 'Walking barefoot on grass is a nice sensation'.' (adjective). The word also brings to mind two classic films: Barefoot in the Park and The Barefoot Contessa.

4 is very natural. 1 would be natural if you left out the word "the" and wrote: "I stay home barefoot all day long." In 2 and 3, you need to add the word "at" and leave out "the:" 2: "I stay barefoot at home all day long." 3. "I am barefoot at home all day long." Another possibility: "I go barefoot at home all day long." "Barefoot" means there is nothing at all on your feet. If you are not wearing socks, but you are wearing slippers or shoes on your bare feet, then you are not barefoot. For some reason, the word is "barefoot", but it means that BOTH feet are bare. I don't know any single word to describe having only one foot bare. If someone had one foot bare, I wouldn't say "she was barefoot," I would use a phrase or sentence to describe it--"she had a sandal on one foot, but her other was bare." Completely tangentially, a nursery rhyme popped into my head. In this situation the child has stockings on, so he isn't barefoot: "Diddle, diddle dumpling, my son John Went to bed with his stockings on. One shoe off and one shoe on, Diddle, diddle dumpling, my son John."

Barefoot is used both as an adjective and an adverb. Your sentence should be, "At home, I stay barefoot all day long." "Barefoot" means you are wearing neither socks nor shoes on the feet. We normally mean both feet.

1 and 4 are both right, the other two don't sound correct. Also you should say "all day long", not "all the day long". Barefoot means you have nothing on your feet at all. And yes, it can be used like an adj and adv.