Hi Eleanor,
With respect to your first question - I'm not sure what you mean by "legitimate demand" - there are no written or unwritten rules in this regard. Whether or not your husband's demand is reasonable depends on what the total contents of your home is worth. Property settlement is not a case of one party demanding something and the other conceding, even if they have a lawyer and you don't. Each party has equal rights to negotiate what they think is fair in the circumstances. So if you feel $10,000 is unfair you should make a counter offer of an amount that you consider is fair.
Sometimes it is advantageous to have a lawyer to advise you in relation to such negotiations and correspond with your ex on your behalf, however it is not 100% necessary. If however you are unable to negotiate a settlement yourselves, you will need to apply to the court - then the family court will make orders dividing your property.
Regarding the second question, legally, both parties have the right to live in a jointly owned home. However, if one party leaves both of you should respect each other's privacy. Therefore, it would be common courtesy of your spouse not to turn up uninvited and this should be communicated to him, and if he doesn't comply it may be appropriate for you to change the locks. However this may cause problems if he still has belongings in the house. Its an issue that you might need to get customised legal advice in relation to.