What icing will stay stiff (even in tropical heat) after the cake has been decorated

You have three options:

1. Prepare for drippage. If you're doing a lot of small items in particular, you set up a wire rack over a sheet pan, and just let it drip down. For the small items, you can dip into the glaze, then invert and place on the rack, like you would glaze a donut.

2. Add a barrier. Make a thicker icing that won't flow, and pipe right at the edge to give it a little bit of containment, then flood the top with the thinner icing. You'll need the cake nearly level for this to work well.

3. Pipe it on. You need an icing that's just thinned to the point where it will slump and flow back together, but not so thin it'll flow off. Use a piping bag (or plastic bag with the corner cut off) to make lines close enough together so the icing forms a solid covering. You may want to start at the outer edge and make a ring like #2, then work inward. This can work for more uneven cakes, as it doesn't need to be perfectly level, but it's more effort to get the consistency right.

Exact technique and consistency is going to depend on how thick (depth) you want the icing. It's always easier to thin it (doesn't take much added liquid) than to stiffen it back up.

It's most likely (in my opinion) that the air (and subsequently air bubbles) is being introduced into your fondant at the kneading process rather than anything to do with your rolling method or surface used to roll on.

Perhaps experiment a little on a more gentle but firm (as opposed to vigorous) kneading method and see if that removes those air bubbles in your fondant.

Are you kneading the fondant in the same way as instructed on the course?