Recommended paint for outdoor cement patio

Rather than just seal in paint that might be lead-based, especially as you mentioned that you're stripping off the bad coat, it might be worth finally just removing it so you don't have to go through these concerns in the future. (especially if you don't have kids now, but think you might in the future, so you can get the dust over and done with).

New York has some recommendations for removing lead paint. The important thing is to keep it from becoming dust and getting spread around the house, which just makes things worse. I believe there are some chemical paint strippers that can be used with lead paint, although that website didn't mention any. I also found mention that Massachusets used to require licensed contractors and require it to be disposed of as hazardous waste, so it might be worth checking before you attempt this.

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If you were going to attempt this without stripping it all off, I'd follow the New York guidelines (contain the area), wet sand to rough up the surface, then prime it and re-paint.

Oh ... and you can also get test kits for check for lead paint. Odds are, being gloss and trim, it's more likely though, and even if the top coat isn't, there might be lead in an older coat.

Putting the brick on a sand base or directly on the ground is what will crack your joints. You want pavers to hold up, lay a 4" base of concrete with reinforcement down first, then lay your brick on a full mortar bed. Then fill the joints with mortar. To lay on sand or earth, forego the mortar joints, and lay it tight joint, as iLikeDirt answered, and pull and spray the occasional weed. A mortared joint will not stay in place, freeze/thaw will see to that....

Here is a pic of my cousins sidewalk, done with a cement base as mentioned above. It has been in place for over 10 years. Long enough for the expansion joints to erode and allow weeds to grow through them. The placement of expansion joints are critical for the longevity of any concrete slab.