A couple of things from the source code,
(do) first() and take(1) actually unsubscribe when they complete
It would appear so.  
take.ts 
protected _next(value: T): void {
  const total = this.total;
  const count = ++this.count;
  if (count <= total) {
    this.destination.next(value);
    if (count === total) {
      this.destination.complete();
      this.unsubscribe();
    }
  }
}
To say an observable completes, does that also mean the subscriptions are unsubscribed?  
In Subscription.ts, came across this (not seen it in documentation)
/**
 * Adds a tear down to be called during the unsubscribe() of this
 * Subscription.
 *
   ...
 */
add(teardown: TeardownLogic): Subscription {
so I figured teardown could be used to verify that unsubscribe is called.
const source1 = Observable.range(1, 10).take(6)
const subscription1 = source1.subscribe(x => console.log('subscription1'))
  .add(() => console.log('teardown1'))
// Emits 6x then 'teardown1'
const subscription2 = source1.take(4).subscribe(x => console.log('subscription2'))
  .add(() => console.log('teardown2'))
// Emits 4x then 'teardown2'
but note that take() only unsubscribes downstream of itself, not all subscribers to the observable
const source2 = Observable.range(1, 10)
const subscription3 = source2.subscribe(x => console.log('subscription3'))
  .add(() => console.log('teardown3'))
// Emits 10x then 'teardown3'
const subscription4 = source2.take(5).subscribe(x => console.log('subscription4'))
  .add(() => console.log('teardown4'))
// Emits 5x then 'teardown4'
I need to know that the observable isn't retaining any references after first() or take(1) complete.
This is a bit trickier, here is the Observable.subscribe() method. Seems the observer isn't keeping a reference to any of it's three parameters, but rather the subscription is keeping a reference to the observable.
subscribe(observerOrNext?: PartialObserver<T> | ((value: T) => void),
          error?: (error: any) => void,
          complete?: () => void): Subscription {
  const { operator } = this;
  const sink = toSubscriber(observerOrNext, error, complete);
  if (operator) {
    operator.call(sink, this.source);
  } else {
    sink.add(this.source ? this._subscribe(sink) : this._trySubscribe(sink));
  }
  if (sink.syncErrorThrowable) {
    sink.syncErrorThrowable = false;
    if (sink.syncErrorThrown) {
      throw sink.syncErrorValue;
    }
  }
  return sink;
}
This can be seen in the following test code. While the subscription is active (closed: false), the subscriber has the observable referenced in _subscriptions 
const source3 = Observable.interval(1000)
const subscription5 = source3.subscribe(x => {})
console.log(source3)
console.log(subscription5)
Console output:
IntervalObservable 
  period: 1000
  scheduler: AsyncScheduler {...}
  _isScalar: false
  __proto__: Observable
Subscriber 
  closed: false
  destination: SafeSubscriber {...}
  isStopped: false
  syncErrorThrowable: false
  syncErrorThrown: false
  syncErrorValue: null
  _parent: null
  _parents: null
  _subscriptions: [AsyncAction]
  __proto__: Subscription
but when we close the subscription with a take(1), 
const source3 = Observable.interval(1000).take(1)
const subscription5 = source3.subscribe(x => {})
console.log(source3)
console.log(subscription5)
Subscriber _subscriptions is set to null, releasing the reference.
Subscriber 
  closed: true
  destination: SafeSubscriber {...}
  isStopped: true
  syncErrorThrowable: false
  syncErrorThrown: false
  syncErrorValue: null
  _parent: null
  _parents: null
  _subscriptions: null
  __proto__: Subscription
I'm not sure this can be considered a definitive proof for all observable/operator/subscriber chains, but is at least indicative of a way to verify your particular use-case.