Generate the answer for a given question. The question requires common knowledge of English. Make sure that the answer is in detail, long, consistent with the context, and requires general knowledge of English. To be less repetitive, please vary your language for each question. Give a proper explanation to answer, and if necessary, provide the definition of various terms. And conclude your answer if it's long. If you have used other resources (e.g., Merriam Webster's.) to answer the question, include citations in your answer. You don't need to paraphrase the context of your resources, but make sure that your answer is consistent and complete.

Invaluable intuitively seems to imply a higher degree of importance. Please explain the difference between valuable and invaluable and in what context you'd use one or the other.
Technically, invaluable works like priceless. They mean that something is of a value which cannot be expressed in numbers. For example great memories, happiness, health, or whatever else you prefer. They are invaluable, because they cannot be sold or bought. They have no price. On the other hand, valuable means something is of a high value, which can be expressed in numbers. Like a golden ring. It's valuable, because it costs $1000.

Looking for a word that denotes both brothers and sisters without gender connotations (gender neutral), in a similar fashion as parents for father and mother.
It sounds like you're looking for one of siblings (as in brothers and sisters), offspring, or children (as in sons and daughters). Sibling (OED): Each of two or more children or offspring having one or both parents in common; a brother or sister. Possibly sib (OED): chiefly Zoology A brother or sister; a sibling.

I live in Australia, but am expected to use US English in my work. I am therefore used to spelling '-ise' as '-ize'. I was a little surprised to find that 'enterprise' is almost universally spelt with '-ise'. Is there any particular reason that this is the case for this example, when '-ize' is so widely preferred in US English?.

For one, because the etymology is different. -ise (-ize) is a causative suffix in formalise, realise etc. (to make something formal, to make something real...) But enterprise is not 'to make something enterpre' or similar (whatever that might mean). The prise bit comes as a past participle of French prendre (to grasp, to take). Another answer is that enterprize is actually attested, and was apparently used more than enterprise in the second half of 18th century (N-gram viewer).