To answer the original question, the normal base height for ACT/DACT is 5000ft agl.
ACT/DACT is classed as all participants are free to unrestricted manoeuvre. All participants are aggressors. The fight would continue until Training Objectives were reached, (for example a valid kill of one player) in which case "Knock It Off" x 3. Anything dangerous the fight stopped by "STOP" X 3.
Below 5000ft Offensive/Defensive Training is termed Evasion Training. The base height for such will vary depending on air force, type, role pilot experience and more. Fast Jet minimum for Evasion Training is normally 250ft MSD. Helo vs Fighters the minimum for helos is 100ft MSD.
During any Evasion Training there must be specified roles of Offensive and Defensive. The Defensive side would be limited to a certain limited number of manoeuvres on turn, speed and height.
In the UK, Training Instruction 4/84 Issue XXX was the set of rules used by RAF, RN, Army and civilian contractors (FRA). Within NATO the Fighting Edge agreement is the definitive document.
Whenever conducting any ACT or Evasion Training one should avoid overflight of built up areas. However, a 2v2 DACT F15 Typhoon may be 5 miles away from a town and still appear to be "overhead" from the ground!!
Some more enlightened supervisors would authorise experience aircrew to perform both ACT and Evasion Training during a single engagement and use the appropriate set of rules dependant on height. This was generally frowned upon by the USAF but willingly embraced by many others to provide more realistic training