The image can talk to any lengths necessary.
Major image places no restrictions regarding how many sentences the image can speak, because that is not how conversations work.
You don't use your action to have the image say a sentence or reply to a question, rather you use your action to have the image converse and as part of that action the image can speak multiple sentences, reply to questions, interrupt, be interrupted, etc. in a way that appears natural.
As long as you are within range of the illusion, you can use your action to cause the image to move to any other spot within range. As the image changes location, you can alter its appearance so that its movements appear natural for the image. For example, if you create an image of a creature and move it, you can alter the image so that it appears to be walking. Similarly, you can cause the illusion to make different sounds at different times, even making it carry on a conversation, for example.
The image doesn't slide across floors, nor does it have a pre-counted number of steps it can take, rather it can move in a way that appears natural. Similarly the image doesn't talk like a recording, nor does it speak a limited number of words, rather it can hold a conversation that appears natural.
Being in combat does not change any of this. Typically, the image will only ever speak during your turn because that is when you typically use your action, but every creature is limited to communicating during their turn, as explained in "Other Activity on Your Turn":
You can communicate however you are able, through brief utterances and gestures, as you take your turn.
Therefore, the image's ability to hold a conversation isn't hampered by the turn order any more or any less than any other creature, as long as you use your action to control the image.