Tile first - its easier to cut carpet than tiles. When finished, using a sharp utility knife, and using the edge of the tiles as a guide, cut the carpet to length.
You can get a special carpet to tile trim (ts called Z or zig zag see Screwfix.com item code 41130) from many DIY shops. but they usually only do one for across doorways, so if you need one longer, you may need to go to a specialist tile shop.
Cut to length and fit. Using a scraper, ram the carpet into the strip.
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busy weekend for you!
Carpet cut with sharp stanley knife, measure your cut and get straight edge to line up your cut with, i.e. good straight length of wood or spirt level.
Do need carpet/tile trim you can get these at floor and diy stores.
I'd lay carpet back down fitting up to trim, then you have a good starting or finishing point to lay tiles, with fixed trim as your guide. You can take carpet back up then if needs be, no real rules on this one. It's whatever makes best sense for cuts and appearance.
Best of luck
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