Equity.  This includes the actual principal you have invested in the purchase of the property.  It does not include any interest payments on loans.

No.  Since you place the lien against your own property in order to secure your interest in the property - in other words, to secure what the property owes you - there is no controversy and so it is not necessary to go to court.  You are simply liening your own property in order to secure your interest in it.

Yes, if the lien is recorded before the foreclosure is initiated.  Once a foreclosure has begun, it is not possible to place a common law lien on property subject to the foreclosure.

Possibly. Liens are paid based on their respective character, regardless of when a given lien was filed. Mechanic’s liens are always the first liens paid. Common law liens are second. Mortgages are not true liens - they are forms of chattel. IRS Notices of Lien are not liens at all. Therefore, a properly recorded common law lien will secure the lienor’s interest in the liened property. Neither the IRS nor any other party (including a mortgagee) will be able to obtain clear title to property that has a common law lien recorded against it, until and unless the common law lien is paid.