Roberto--this is what I hear when I listen to the High Atmosphere recording (my additions in parentheses):

Come in, come in, my own true love
And stay all the night with me
For I have a bed and a very fine bed
I'll give it up to thee, thee
I'll give it up to you

I can't come in, I (h)ain't a-coming in
To stay all the night with you
For I have a wife in Old Scotland
This night she weeps for me, -e
This night she weeps for me

She (so she) drew her little penknife
She pressed (pierced) it through his heart
She cried out with her low, low (loud, loud) voice:
There's a dead man in my house, house
There's a dead man in my house

She picked him up by the middle very small
She picked him up by his feet
She tossed him (over) in a deep dry well
Just about eighteen feet, feet
Just about eighteen feet

She was headin' in her ... (sittin' in her poor ) little door
Thinking on what she had done
She saw a pretty little bird
All on the leaves so green, green
All on the leaves so green

Come here, come here, my pretty little bird
And perch all on my thumb
(It's) I have a cage and a very fine cage
I will give it up to thee, thee
I will give it up to you

I can't come down, no I (h)ain't a-coming there
To perch – said -(perched) all on your thumb
(Cause I'm afraid) For you'd rob me of my tender little heart
Just like the Scotland man, man
Just like the Scotland man

If I had my bow and arrow
My arrow and my string
(It's) I'd shoot you right to your (the) tender little heart
Just like the Scotland man, man
Just like the Scotland man

If you had your bow and arrow
Your arrow and your string
(It's) I'd fly away to - heaven so high
I'd never be seen any more, more
I'd never (ne'er) be seen any more