Is this a too good to be true scam or a real deal holyfield blessing?

This may be long-winded but bear with me...I was contacted by this lady thru email because she saw my resume on CareerBuilder. She offered me a position as an USA Administrative Assistant. Her company is an art gallery in europe and she is the senior manager. Basically the job entails, as per the email correspondence with her, " Some of our customers from the USA are only able to send the payment locally by the US cashier's check.
That's why we need a Administrative Assistant in the USA to process payments from our clients.
The job is part-time and requires 2-3 hours a day. You will receive paychecks from our clients at your mailing address weekly, deduct your commission and forward the funds to our representative office by Money gram.
Usually there will be 5-6 paychecks per week.
Once the paycheck arrives, your supervisor will notify you and assign your tasks for the day and will give you instructions on forwarding the money to our company representative office.
Your commission will be included along with every payment. We will let you know how much of the paycheck amount is your commission and the amount that has to be transferred.
All payment processing fees are compensated instantly and deducted from the amount received.
We also pay all tax expenses and transportation fees."

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One question that pops up in my mind is that why cant the customer of the artwork just send a moneygram themselves and why does the gallery need a middle man such as myself? Thats my only real hangup right now and my GF thinks its a major scam, but here are some counter points to the idea of a scam...from our emails, " The company covers all expenses, you are not required to invest your own money. You are also not required to pay any start-up fees.
We provide a one-month paid training period, during which you will receive online training and support, as well as a regular paycheck.
During this time, you'll receive all the necessary instructions and training from your supervisor. One week before the training period ends, your supervisor will be making his or her decision, regarding whether your performance has been satisfactory enough to offer full time employment. "

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So basically if i suck at the job there is a high chance they don't want me to work with the company. Also I do not have to put up any of my own money to get started which seems like a huge plus.

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More email correspondence, " Please, kindly fill the application form and sign up the agreement (attached to this message).
You don't need to invest your own money to get started. We also do not ask any secure details from you."

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The only things they asked of me was my name, age, address, phone number, education, and employment history. Never asked for a social security number. Also the agreement form looks super legit and written by a lawyer of some sort. I can add the agreement form later if anyone wants to see it.

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More email correspondence, " We can pay your salary by direct deposit or paper check. " I feel like them offering to pay me by check is a plus because it shows that its okay if I dont give them my banking account number.

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Now down to the pay rate which to me is a crazy amount for something as easy as cashing a check and sending it to the gallery, " Your starting salary will consist of $2000 regular monthly payment + 5 percent commission, which is deducted from each transaction made during the training period. Total income, considering the current volume of clients, will be about $4000-$4500 per month." " Your commission will be included along with every payment. We will let you know how much of the paycheck amount is your commission and the amount that has to be transferred.
All payment processing fees are compensated instantly and deducted from the amount received.
We also pay all tax expenses and transportation fees."

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It seems crazy to me I can make ~3k a month just for doing this simple task.

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I have looked up the gallery and its a legit gallery in europe and the address she provided in the email is the same one as the website's. When i googled her name or email nothing came up for them, which i guess is good.

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I am a broke post college graduate with a heap of loans and an average at best credit score; I really cant see anyone stealing my identity when I imagine you cant get a loan or something along those lines from a broke college graduate with a so-so credit score. Also my father passed away two weeks ago and I never posted anything online about it, so I think I can rule out someone using that knowledge to scam me.

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What do you guys think?