Are milk teeth characteristics such as shape, alignment, spaces between teeth, etc. indicative of what permanent teeth will be like?
No, the characteristics of milk teeth don't predict much about the adult teeth.
Disclaimer: I have no dentistry education; this is my personal experience and beliefs.
Milk teeth are smaller because they start out in a toddler's jaw so by the time the child is six, they'll have some gaps between them. These gaps disappear because adult teeth are bigger.
The adult teeth have different roots than milk teeth, so their alignment is brand-new and not identical to the milk teeth.
One of the things that are closely linked is dental health: If there were many dental problems with milk teeth (fillings etc.) because the milk teeth were treated poorly, not cleaned well, or weak by nature, then that's likely to continue with the adult teeth.
Take good care of your teeth; only sharks can regrow them.
The only thing I can think of is when permanent teeth start popping out, milk teeth can be on their way hindering permanent from growing in right direction.
Besides that, as Torben said, dental hygiene is important for milk teeth, to make a good habit of it in future.