Yes, if property bought as separate property was transferred to an individual living trust, it's still separate property, as long as the other spouse hasn't contributed to its mortgage, upkeep, etc.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
If living separately, the purchaser's income would be separate property. But the status of the property purchased would depend on what was used to purchase it. The purchaser alone can't determine the character of the property merely by telling the escrow co. to put "sole and separate property on the Deed.
Putting it into a Trust does not change the character of the property unless the Trust instrument says so, or there is a written property agreement as to the character of the property.
Yes. Real estate which was purchased as sole and separate property using separate property funds remains separate property when transferred to an individual living trust, so long as community property was not used to support it such as taxes, mortgage and repairs.