Applying grout colorant is tedious but not difficult. Fortunately, the setup is easy so the job doesn't need to be done in one session.  If you like to occasionally zone out on a mindless task, this definitely fits that description.  Or, find some companionship,  put on some good music, and consume your favorite beverage and get busy. You might want to find some kneepads because tile is hard on the knees

They jack hammered the old brick out. And there was a subfloor they were able to put the new wood down over. We had the entire house floors sanded and stained and sealed at the same time. The floor guys used different stains ( or clear stain) and were able to have the color uniform though out the house. What was really impressive is the upstairs bath was black marble floor with 2 inches of cement under it (2 inches!!). Under the cement was the original pine floors from 1800s. The demo team was able to get the marble and cement up and leave the original hardwood floors. After sanding and staining -they look fabulous. Never thought I’d love hardwood floors in a master bath - but I do!

No matter the loose bricks need to be fixed anyway so get a pro to do that and also redo the steps . Or fix the bricks and have a concrete cover put on . I have no idea what the style of your house is so can't really answer this question BTW is there brick somewhere else on the house ? I would not do trex for sure.

One drawback I see to making a patio at ground level is the inconvenience if you need to attend to a bbq grill.