I'm not shore why you need to take the subfloor out?
What do you have now for subfloor.
What are the tiles now on? Probably same ply that carpet is on?

Jetswet~good question. I have no idea what type of subfloor it is. The guy at Lowe's told me that the tile floor would need a subfloor. Now would this be the same as what they need to do to the floor that has carpet? I'm clueless:-)

Also, does anybody know if it's true that you can seal laminate flooring to keep liquid from getting into the joints? Just wondering if this is true or not.

Well the real answer about sealing laminate is no, there is probably stuff out there that you can use to seal the joints but I wouldnt recomend it.
I have laminate in my kitchen and dining room and as much liquids spill I don't have issues, now I wouldn't put it in a bathroom.

So as for tile is concerned the recomendations of instill is to use a cement board between tile and subfloor for a filler, a bond to hole tile down. It's possible to tile right on plywood but you will need the correct ply and subfloor needs to be strong enuoph 1 1/4 of plywood from joist up for Standered recomendation.

That being said I do not know what is under that tile now or what they used.
Taking the carpet up and putting down laminate is fairly easy if you know what your doing, tile on the other have gets tricky.
It looks like the ajasent room is all the same tile?

Yes, that's the sunroom and its all tile too. How about this scenario? Can I just get the laminate flooring and have them take up the tile and leave the tile around the fireplace and in front of it [maybe 2 tiles width all around it] and at a later date change out the tile? Or, should it all be done at the same time? In other words, would it be a bad choice to have the flooring put in first and then do the fireplace later? Or, should the fireplace be done first and then the laminate flooring?
Since I'm putting new flooring in, I just wanted to update the tile around the fireplace as well.

Thanks for your help!

If I was you I would go with a color laminate that is close color with your existing carpet, leave the tile around fire place, take the existing tile in other room & let us know if there is just plywood or cement board. But the morter that is on the floor from tile that you take up will have to be scraped & maybe a belt sander to get the floor smooth for laminate.

Take the carpet out and post close pic of tile end and subfloor meets.

I've decided to use a wood laminate [Fruitwood Spice] but I was thinking that since I'm taking out the tile in the sunroom and the foyer, I might as well change the tile around the fireplace to a newer look since the floor will be new. Are you suggesting that I don't change the fireplace tile? Is that going to be a problem? I'm not doing the work myself; I'm having a contractor do it. I'm just trying to figure out what is the best and easiest [economical] way to go about this.
My next door neighbors put laminate flooring in but they bumped it up to the fireplace. I don't want to do that. These are wood burning fireplaces and I think there should be some tile around it.

Question: taking up the tile in the sunroom...is this going to be a long, tedious job? I guess I don't realize all that's involved.

Since you're tearing out all the tile, I'd do the demo all at the same time. I wouldn't hold off on the fireplace tile until later. You'll have to go through the mess twice.

Well if your have a contractor do it you will be at ease lol
Your correct might as well change the time out as well.
Questions you need to ask him is to make shore there is adiquite subfloor for tile even though there is tile there now doesnt mean it is.
Find out if there is cement board for tile to bond to or will he install on plywood if so why kind? B/C sanded or A/C plywood is what will work C/C is what's recommended but to hard to find and $$$ as well.

You you need something that will not catch on fire Infront of your fire place by code x amount away I forgot what it's called but you do need that if you have carpet or wood floor.