OP I am really sorry to hear about this.
I rent out a villa (which I manage myself) and I have the following comments:
a) parasols are replaced every 2 weeks - they simply DO tear and fade in the sun/wind/hot weather. This is in no way your fault. They should have been new when you arrived frankly.
b) I ask for a security deposit in very rare situations such as pets coming or if I feel the family are actually inviting lots more people than they say who will be sleeping on the sofa etc (it happens and you can tell the people who are going to!)
c) If asking for a security deposit, as another poster says - you give it back there and then having checked out the property first.
d) Included in the rental surely, surely, cleaning on your day of departure is up to the person who has rented it to you. Even if people leave a place spotless, you still have to go through everything, defrost fridges etc to get it ready for next people. It is ridiculous for this agent to say you left it a tip - makes no odds - still has to be cleaned.
e) as another poster says, a lamp breaking, plates, glasses, it is all par for the course. The worst that happened to me was a glass patio door got smashed, then replaced, on insurance the next day. I did not charge the people staying anything.
Having said all that (I am cross as it gives people who rent out holiday properties a bad name) I will say the following... I think it is the agent trying to make money. I am sure of it. She is reporting back to the owner and is ripping her off too - I would bet money on it.
Before I took over the handling of our villa it happened all the time with cleaning being massively overcharged and badly done, laundry, garden, pool - you name it. Your absolute best bet is to try and contact the owner direct or INSIST that the agent does. You threaten her integrity and reputation as that is what we all rely on. This will worry the owner (quite rightly) and she will hopefully back down.
I would also complain about the flies, again - their responsibility.
You also ask for receipts for the replacement of the lamp - how much can that be? How can anyone justify 400 euros? The parasols, swing and a set of laundry are totally par for the course. (So is the lamp IMO)
Good luck. Remember the owner is doing this as an investment and you can really say you are going to make trouble. If you can't get hold of her directly you insist the agent passes on your email and ask for proof.
HTH in some way.