"Tu ai înota împreună cu mine?"
Translation:Would you swim together with me?
would + infinitive (would sing) = aș/ai/ar/am/ați/ar + infinitive (aș cânta)
would have + past part. (would have sung) = aș/ai/ar/am/ați/ar + fi + p. part. (aș fi cântat)
'Inota' is with only one 'n'. If it was with two ''N''s, then it would have been a derivative from the word 'nota' wity the prefix 'in'. That, when you have a word starting with 'n' and you ad the prefix 'in', is the only time you'll see a double 'n'. So not for Înota.