Answer: Congratulations on the blooms on your Murraya, that is so wonderful! As far as pruning, cut off any dead twigs (dry, brittle, discolored twigs) and then trim a little bit more if needed to give the plant a pleasing look. Each cut should be made just outside (just past or just above) a branch to avoid leaving long, bare stubs. New growth will eventually hide the cuts.
The money tree question is a judgement call. It is never good to have a pot without drainage holes as you know, excess water trapped in the bottom of the container is not healthy. On the other hand, this is not the best time of year to repot and as you mentioned you do not want to shock the plant.
How much to water depends on the type of soil mix as well as the size of the pot in relation to the size of the plant and also the humidity and temperature of the place where it is being grown. So there is no rule to give you on the amount. Watch your plant and see how it responds. I would use tepid water, apply it very slowly, take care not to saturate the soil but try to keep it damp like a wrung out sponge. Hopefully they put a bit of gravel and horticultural charcoal in the bottom of the container to try to allow space for excess water to collect away from the roots.
When it comes time to repot, you might be able to find a pot with drainage holes that fits inside the decorative pot so it looks nice. (Raise the utilitarian pot up off the bottom of the fancy one so it never sits in water.)
The straw or whatever material on the surface is just decorative so you may discard if you wish. But, as long as it is an air permeable material and does not touch the stem it would not contribute to root rot.
I hope this helps!
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