Set the tile so that they end a bit higher than the height of the tacks on a tackless strip. Then you install tackless strips around the tiled area with the correct spacing and attach the carpet like you would at a wall. If you are worried about the corners of your tile not being strong enough, they do make some metal transitions that only have about and 1/8" or less showing on top so they are barely noticable. You would still set the carpet as I described.

Personally, I don't like the look of a Schluter strip. If the heights are the same, I would have the two different types of tile just butt up against each other rather than go with a T-moulding. That's just my personal preference.

I'm seeing 'peeling paper' on the floor. Are these peel and stick tiles? If they are, there is no need for a transition strip. I agree you should patch that bit through the doorway. Only floating floors require the transition strip. If these are 'fixed' by adhesive then there is no need for it...other than to deal with large gaps or holes that are too large to patch/span.

I'm not going into all the details, just an overall view. You have a lot going on in your living/dining area and the walls seem quite dark. I would suggest you paint the wall in a lighter colour, perhaps get a wall unit (on the wall you presently have your TV) flanked with 2 comfortable chairs. You seem to presently have a beige area rug in your living room that perhaps can be moved to the dining room to tame down all the different chairs and colours in that area. Sofa in the beige/greige tones with area rug (muted tones) and accent pillows to tie in with what you have in the dining room. For more impact, less small objects on your matel. Have a look at the visual that gives you an idea...