Let's leave faced to one side for now. It's an odd verb that has some quirks, and your second example is actually easier to use to describe the issue at hand.
Now, your other example doesn't involve two natural English sentences (the first doesn't work, for reasons that should become clear). However, I think I can see what your issue is. Let's look at the different ways you can use a -ed form of a verb. There's going to be a bit of a meander here. If you feel complete fine with the difference between past tense and past participle, including using verbs that have different forms for these two roles, feel free to skip from the bit between the lines. Dangling participles, which is what we are talking about here, are also mentioned briefly, but we'll look at them in more detail after this background.
Two forms of regular verbs are formed with the -ed suffix. These are the past (used in the simple past tense) and the past participle (also known, among other things, as the perfect participle, and used for the future perfect, present perfect and past perfect).
I finished (past simple)
I have finished (present perfect)
I had finished (past perfect)
You can also use the past participle as a dangling participle to add description, generally as an adjectival phrase - because the past participle can function as an adjective.
The book had been sent to the publishers, finished at last.
Finished earlier that day, the book was in the hands of the publishers.
Now, this distinction between the past simple and the participle is not purely to do with syntax. There are a fair number of verbs that are irregular in the past, and then the past and the past participle do not match.
I see the movie.
I saw the movie.
I have seen the movie.
I wear a suit.
I wore a suit.
I have worn a suit.
Finish is regular in the past (and everywhere else, I think), but it's still important to know what you're doing.
So, let's get back to the idea of a dangling participle. These are also known as participle phrases, and are essentially a special sort of verb phrase. They have as their own main verb either a past participle, or a progressive participle. The latter sort is actually more common, in my experience:
Seeing the red light ahead, I slowed down.
The principal verb of the sentence is to slow, and the participle phrase using the progressive participle of to see. It describes something that the subject of the sentence, I, was doing at the time the sentence refers to. It could use a verb that indicates state, of course:
Hating to walk, she hailed a taxi.
In this case, hate is still a verb that applies at the time of the main action. Past participle phrases work differently:
Hated by everyone, Bob didn't have anything to do on his birthday.
Here, the subject of the main verb, Bob, isn't doing the verb in the participle phrase at the time of the main action. Bob is described by the participle phrase. It functions as an adjective for the subject of the main verb. You would expect to be able to use to be to summarise:
Covered in yellow paint, the building cannot be missed.
The building is covered in yellow paint. The building cannot be missed.
Obviously, pulling it apart like this loses some meaning; the use of the participle phrase suggests some causation between the participle phrase and the main clause. However, putting it in these two separate sentences helps to see how the two relate in their most basic meaning.
In your example, you cannot say "I am finished the book". However, you might say you are finished with the book, so if you really want to use a past participle phrase, you could say:
Finished with the book, I had a holiday.
The second sentence in that example, it is a progressive participle phrase. You had finished the book, so you can use the progressive participle of to have. To finish might be main verb of of the participle phrase, but it is to have that forms the participle. This is essentially creating a progressive participle phrase out of a past or present perfect, and the tense of the 'separated' version of that participle is set by the tense of the principal verb:
Having finished the book, I had a holiday.
I had finished the book. I had a holiday.
(As an aside, you could get something nearly the same as the first version of your second example by using a differently structured phrase - you could say "the book finished, I had a holiday".)
You could also just put to finish as a progressive participle, but this doesn't quite work:
Finishing the book, I had a holiday.
That suggests that the finishing happens at the same time as having the holiday. That can work, but if you wanted to suggest that you started your holiday the moment the book was finished, you'd be better saying:
Finishing the book, I went on holiday.
So, back to your first example. The first version is a perfect use of a perfect participle phrase:
Faced with a bill for $10,000, he has taken an extra job.
He is faced with a bill for $10,000. He has taken an extra job.
The second version introduces having completely unnecessarily. You can just use to face as the progressive participle:
Facing a bill for $10,000, he has taken an extra job.
This means that he has taken the job while facing the bill.
If you really, really want to use having, you need to find a way of putting where you can say "He has/had...". The way to do that with the idea of facing this bill would be:
Having been faced with a bill for $10,000, he has taken an extra job.
He has been faced with a bill for $10,000. He has taken an extra job.
Participle phrases can be tough to get your head around, but they are widely used - if not widely understood by native speakers who are using them.